Physics
General
Easy
Question
A Particle of mass m is at rest at t=0 The force exerting on it in x-direction is F(t)=Fae-k. Which one of the following graph is of speed
The correct answer is: ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANsAAACNCAYAAAA+VA+qAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAFxEAABcRAcom8z8AACj2SURBVHhe7X2HW1RJ1v7vH/l2v03fBEcnx3VGZ2ZndV0dHQMoZhRBRYIoCCgKKogKqKCIkkSy5JyUjIDkHCRnmpy66QbeX50CZxxnRhBRG6j3eeppuLfu7dvd9dY5deqE/4fXjPHxcVhZWeFPf/oTdHR00N7ePnVmdigpKYG+vj6WLVsGU1NTjIyMTJ0REFAuvHayTUxMICkpCdra2ti8eTNsbGzw+PHjqbMvhqqqKlhbW/P76OrqIiEhAQqFYuqsgIBy4bWTjSCXy5GdnQ0tLS1s3LgRrq6uqKioQHd397RkIbL29vaitLQULi4u2LFjBzQ0NJCamsqlpoCAsuKNkI0wOjqKtLQ0XLp0CYaGhjAzM0NgYCC6urqmevw+iKgxMTEwNzfnauO1a9eQnJyM4eHhqR4CAsqJN0a2JyAV0tPTE3Z2doiMjERPT8/Umd8HSb7ExEQ4ODjA398fNTU1U2cEBJQbb5xspBaSVBoYGODGDVIF6RhJsKHBQQz092NkeARjY2M/95dKpT/3p/8FBOYD3jjZfg9EtLa2NuQ8eoTkxCQUFRSiv69/6qyAwPyEUpKNJBYRzZ6tx0xPmMDl1m3U1tROnRUQmJ9QSrJ1dHQg4N497N29Byu//gbaBw8hLTV16qyAwPyE0pFtaGgIuTk5sDp/nhPtr3/+X6xZtRquzs5obWn5ee0mIDDfoFRkI+PI4+pqeLi7Y++u3fj4gw/xt//9C5Z/+RX0dHQQEx2Nvt7eqd4CAvMLSkW2wcFBJMTH47iBAb5bsRLvv7cUy5a8h88+/gSr//1vXLCyRHlZGSbE5rXAPITSkE02KkNlRQVuODhgw7ofsfTdJZxon370MT5c9j7/f9eOnQgPC4NEIhHqpMC8g9KQrb2tHRFh4TA0OIZvv1mB9955l5ONVMkPli7De2+/i/+u+g8uXbyIHLamIykoIDCfoBRko43pivJyuNxyxpHD2lyykRr5xaefccn2zy++xL+//xdUN22B0XFDREZEcOkmNrQF5hOUhmzNjU18A/uevz9cnJ1hee4c9qurY8vGTTioqYkrtnbwuuuJgHsByMvNRX9/vyCbwLyC0qiR42wNRp4jMpmM+0c+zMiA/dWrMDU2xi0nJ5QzyUfnqJF/pCCawHyD0pDtWfAQmtu3cdbCAl6enmhrbZ06IyAwPzFFNiYlxuUYk49gZHgYg0MjkMpGmBQZxGBfD3q7utDd3YPu3kH0D8sgVYzj18Z3dv0YkzjDfRjopr596BsZhXR8ArOxGdLGNhlBHK9fh9mpU3BzdUWt8O4XmOeYItsYJsaGIO1vRVtdJSqKilBSVIjikgIU5OUijw38R48escb+Lq1GVWsvOofHGJkmr2ZMBaQSDDTkoTA+BglRaciobEOtdAxD7OyLKnxENnq/G4xsp06ehKuLy6yjuQUElAVPSTYpFH11aCuOR3qQK5yv3oTDLT/ci0vEg6wspCbFIjHsLsJDghCaUoq0xyNoZkyaJBIjm6IZPZURiLhsicsm9nCOLUR67yg6J8++EATZBBYinlqzMUqMNGCg1BcPHI/i0EYNqO63g0M8I1pjI0qL0lAY64hIH0e4BmXgXlY/yhiTJolElGtBX00gvPQPQme9Psw90xDVLUcHP/9iEGQTWIh4imy07mqGvMYTSQ77oPLZBnyz7gKuPaxGkVyO7q46dJeFoyA5AOEP8hGVN4hqItvPOmInhlrD4KWtDs2V+2HskohQySja2Jmfu8wQgmwCCxG/JhujxliLPzJuH4TaZ5vw3YYrcC7tRCOdnZACg4xwLRWormtHdcsoukmN/JlJvZB2JyDAQBNHvtsNo+sh8KpqRkmXBO2SbnT1DGGAreHGZsA8QTaBhYhnyNaOsfYQZHkcw/4Vu7BezQl3q3uYzBrDxHgfhvp6IZEMo7dPAZlsgh2bvHISAxjtTUH4qSM49oMK9M/YwDrwHtxDfOHtEwCf4DTE57eiaVAxraQTZBNYiPhDsmms3I51Kg5wLmhE43g9OlozkZtTjozcXtS3jmNUPnnVLxiAvDcVEWe0YfDtGhw4qA3dswbQ09+FPWrbsWmXGfTsExBZ04fnp/QRZBNYmHiGbB0Ya2Nku6MLja/X4dvvDXHKMwwRD90R6mcNO6dQOAY1Irt6HCO/Se9IZEtG2KmDOPrdBhw2tsR5LzfccDqP87o7sOe/66Gy3wKnwiqR1guMPke8CbIJLET8lmxMsmV76EBj+Sr880tN6Njewm1vazhdOwkL+2DYhzQgq0qKQakC42zB9osm2Y/RniSEnNDC0dV7YXIrFsHtUjT0NaMp0RHBx/4L3e07oHIpBY7FExh8zm73s2Rzd3NDfX391FkBZQSFPFEuUKlMKlzq/gC/VSPbgplk02Nrto344T9nYB2ZgdSKR8jLT0RSVjnScptRVdmAjuZGtHcPoHMEkHPG9UFOZDM6DIM1mjjtkYqoYaIgE4HVISi+ug3ntLZhnVk0LFPG0P8bNfQXDD5FNvIg8bhzBy0tLVNnBd40xsbGIZPKIB2R8jSDvT09fDIsKiriv1t+Xh6PuJd0dvKJk1IPUl8pu0YhX7wk/I1km5CEIcf7BDT/pY6NO13gUzuAyRzFw5APtqCzrhRlOY+QmZyN9LRSFFZ0oHVYBjkGIetNQrDhEUa2g7DwTEH0ENkoGRurI1B1Ux12BnuxxTIe1mnPJxv9QOSuRWQzMTbG5YuXEBoSwt4vDQX5+TwhEP2AnezHLC4s4smAsjIzUcNUTUmnBK2trbzgRubDh8hkx0kFpSgByk9Jg4KOJz1IREFBAS/sQWnPqQ9l9CIH6KLCQu6LSc9BTtGl7F7UPyU5mSeFpZyVlGqPrn+Y8RCPsh+xwfUY3V3dPNdlc3MzO5bNo85zHuXwLM8Uf0cDkJ4zIz2dvwflVKF79XT38PTrdP+kxERUs370rHRdIeuXmpLCn5mup+eha5qamtgaOpf1T+LfFX0n9N71dZOfL5E9L52n74I+R5dEwoNz6TMSGZrZ9dKRkcnvhF0z+dkfsucq4u9Pz5Obm4uH7F6UuZqe4cH9+zy8KcD/Hny8fHjz9vSCm7ML7Gxtceb0GZwwMsIpU1NcsrbGbScneHp4sD6e7PUugoOCUV5Wzh3OFyN+TbaJNoy1BiHTXR97lqthjcoNuFf0YVKm9AOSdDQVRSImNgl3PJNxzzkCSZEJyGruQBtGMdSXgjDDQ0yN3I+TbgkI61agfaQHQ/nByLXThO0JHRxyzoZLBZNez1EjaQBQGA35Rh47agDdIzo8zk2PvV68YM0JRESjAXLV1g5HDh2GidEJ+Pv68YFHg5aIanjsOE4YGsHP15eThAZeWGgoP66+ew8j8UVkMHIVFxfD18cHZ06Z4Zj+UdjZ2PLBRaQhh+gb12/w/loHNPlAq62tZQRP45MAPZ/ZyVP8eiJ+U0MjJ9kp05PYpqIKczYAaYJobGjgfUzYYNTX1cMVNjiTHjzg9yotKYWbqxu/P72Pj5c3JztdZ2tjg8MHD8LQwAC+3t6c+HV1dYiLjcNZi7PYt0cdFuYWjMRZaGps5AG49Jn3qe+D1XlLRuwMPqEUM6lDa1+j4+w7OW7ISUATQkZaOq5fs4fmfg3s3rETJieMebQFva8x+051jhzB4UOHcEhLCxr79mEnWwpsU90KNdZ2bFPDdtboc27+aSPWr12Htf9Zgx//uxYb12/A1i0qrK8qVDdvweaNm9jnOISoyEiuZi5GPEU2OSaGKtCbew2BZj/iuz99hrc/N4RJdCWyR8EkSTvGy/1RnuAGr6B42N9Jhq+DB+I9XBCQ9xjZinH09Wbg/qm90Fu5FvtPO8M2tRjJhZnICnOFvyWb7S444HpSDR4OPN9AMsxmYiIbpUg4zgYzDU5qFMVte9mWDxIKHqUsXA5soBzV02MD/uRUrFseJ4rTzZswNTbBSTboKS0eDerW1jY+M9NxTY0DfDYm4tIAvufnh3MWFjBmA9X+6jVOJlJdy8rKeIgP9ddhhA8OCuKDPSMtg11vxwekhbk5u94fJUXFaGYD/gEjkcUZc+zeuRPnz55DIZOAjYyE1MeMPQ+R3YFqFCQloY49V1lpGe6ywU8TCr0PTRokOYvYddfYwNfT1YXpCTaZsGck8pN0TohPgJWlFSeo5bnzyM5iZGPSipIimZ8+DV0dHdiz74YmEpq8yJHb9bYzNNTVOTEOM/KcMTvNn4XIsfSdd7Hk7Xew+t+rsG/vXmhpavJUgvtYfyKaLiOdAfuejVh/Cns6c9qMf0bzM2fYKzVznGXfw5P25H96FvptTpqYwObyZT650dpuMeIpsskw0V2E1mRbeJtsxLr3V+DT741geC8fSUwT7O9vhDTFGTl+1+EaeB+OQRmIdHdFossVOCWUIIQJvt6BMpS5nsClXao4ZHQZZh6h8IwIQoD3Hbjc9IJ7YAYyG3q56f95WjupPUQkIpsxkwSW58/D864nm81j+UxNEmd4aBgt7JXUPpotSZoUF5dwgtQzMtDgo/7xcXS8eEr9GuSqFB0PDg5GOlPnaIB2Ts38iYwksTEx/J40oEn1JAlKFXdCWH/Kf1LGBjvdq6G+gam16bw/qVfFjGjtjCB9fX1citIxInli4gMuUft6+/h7JLDnIULQe9AE0MNUWHoPkmLh4eH8fehepHYS4WhwRrAJIo69D62J2pm6SFV8SO1NSmZrZKZeU9AtqaT0vdWwexLZQ0JD+GtVVSX7vkjlzIELI5u+ji6TTtuxVUUFWzZtxoYf12PN6tU8XSBJI/U9e7m0JrIQOSjMyZ9pBhHssyfdf4BHWdl88igrK+UxhpSAiRpF2tN3+6TR/0/O02RGaj2V+CLVeLFWG/qFbBOjGB9oQFdpDNLv2cPewhrnbPzh+7AOZWwiGuluwFDcTWR62sM56AGcIjIR6+WKJGcb2McUwrsD6JNJ0JcXikSP63B398Gd4CiEMRLEPUhBfFoJsssk6Bqa2aY2qYhENpoRSSWkAU8/VC8bzLReI+sXrTlovUWDktYsfX39/BzN5ESI9o52fpxIQ+sEWpwPsvVOByNXCyMA3Y+yL5Na08/uS4OerqG1F93j6WBWIgy1gYHJe9F5up5UtM6OTp4end6bztHzd3Z28EmhU9L583EiIj3Pk3Ui3YNmeXoPOkefo7WllT8vWfOk7Di9Rys7TtdQn5/fY3gIki4Jv4YIKx+V80FMz1pZWcknkri4OEQwAvsw9ZPUVlOmIh7V08dRfX0uLXW0j8CQqZUXLC3h5OgID/c78GYqbFBgEJ+QaEIgokxqBWzCYO9PzyqXj/Lne7aNUWO/y9jYb88pFOz7Z6+LuazXU2Qbw4R8CNK+NkiaHqOmohIV1U1o7BpCP/t+xnqbIEt1Re69G3ANiIG9XxKCbjkj7vZV3E4qRnA3MDDOiDTIBlJjJeoqSlDO1KPyqlrUNHeipXsYfcPjz3id/D6etUbSWmOxVquZbmL6GawjEY3UzHhGMs+7d3n69nNsPUdq9v696kx1PMhUOwuuYtN5UrtJmpeUFKOxsWFyQmFkJwKTQYUmJiKXyGQ2N3hKjZwGUglQE4XqNG/cC46Eg0s0POw9Ee3lg6iSOuQy6fcrTXycSR8pBaGOkfH/hfAs2XjwKJtdBX4LSidB0rmuto6r0tenVG+SWrTOJWMIaQe0rnJ0uM4lHWkJJP1I5SbpKvB6MHOykQl/tBySxlSkJSXCz/s+7t2NR0piFio6e6Z1wXoRkBr29KY2kU3UYfsFpIrxNR2TRBXlZdwgRMmQzM1O8zWXCluL0StNVM5szRUTFc3N/Q0NDVzlfKK+LmaV7k3gBchGYD/QWDe6W5tRU9bIFsJtaOlkqsbU2bnCs2QT7lq/gDaEaW1JhiJ3NgmdZoQ6xNRDSmC7e8cuvg1iefYc7nrc5SoiGSi6u2mndMYKqcArAicbzXRkfctjsx+Zwmmg037V0+1RTi4e5ebzjdL87EfIY6rIo9xcZOfnIYddR6kTnr3m6UaqCzXaKH2yMfxHM6sg229B3xUZS2gjnfb6aO1F9RAox+amnzZySUbHggOD2CRYiaHBIb7WEi5TygNONhrIN9mimYrBr1q1Chs2bMCmTZt+1TYy1WTjJhVs3qyKrSqq2LaVvaqpQoW9btmyGZuf6f9sW79+PdauXQtVVVVcvnyZm7Fp8f17EGT7Nai2Ae3TBQUE8iS1RC4y02tpHOAb64HsOHnXkBSTdEqEeqik4GQj95zrbGATEVauXInVq1dzYsxlo3v+8MMPnMgXL17k+y5/tLkpyPYEE9w6mJKUBIer1/gG9sYNP0Ft61amPppxCUd7V2RSF1B+cLKRSkcbkLQJShuoUVFRiI2NnWpxiIuPR3xCAuLplbcEJLD/ExLiuQWMjsWxY9SHH4+PQ3zck+snG92TGvUlotEC/49UnMVONiIPfQfkCxl4L4C7opHL0w41Ne6tQoX+yTpL5bNoz01gfoCTjQY9/WhkQiYSUKMfe2h4BMMyBeTjE3x5Tf0m6O+fOcL+mKBNzHEoxvh/k5hQYEwuhXSY3YPuw9qT+9L6cLoBspjJRhvHtG4mAwc585JrGbmpkSGE0rKTY3CPqFE3L8HJ9scYZ7xhZOnphKR10kujo7MVbS0N3OG2vkmCFskABvq7MdjdiNaGWjyub0OjRIpB+e9LrZlgMZJNJpOiob6eS61zFmdxYP9+7hxM/prkLkW+orTZTBOiwPzENGQbglxSiOJoHwTdvAVPHz/4hbLmcwvON67D1t4XTt73kZgSi6z7rvC7fRmWF91w1ScHaY/70DvLdfpiIxtloaaQGyplTBvRZFk8zqTZdXsHrpLXPKaQm6E/VLsF5gemIVsvRhrjEXvxCEw3bcIhPROcuGoLS5uTMNXRwK7NWtix/xwu3HSCj68VbM32Qe1HdWzZfx32MeUoGhzDbPwTFgvZaG1GcWXk/U+hQiTJtm9V4zFhVM2H/BJpj0yuEOuyhYBpyDYMWWca4iz24OjK5diuZQYjz1C4hnnC9dJxHN/wE1TWauCIrQc80iMQ7HsBpps3Q2WVNozdkhDZLkUrm4xfVMAtBrJRpDNZgSkygGLf9uzcDU0NTV7skZyAGxobhZVxgWEaso1hbLgSD+10cHbdKhw66QS77GZktdehPNENvtpbobtlL444xyOotxv1jRmIOqEBwzXbcPx6ODxqB1HNmPai8/JCJhupghQiQ5vTFOVsYmiE3Tt3cbO+4w1Hfpy8/oXz78LDNGRjUknRjNybJrBT2wSjS75wrVXgMaNPb3k0ksz2w0JdC4b+2YhlfaXjDSiy0YfVRhUYOYTApWoAFWxyftFQwYVMti6mFlLqA4oGp8hlba2DsLK05EGplIpASLOFi+nJJm9EjqMpI9sWGNt4w7VmBKXyYbTkRyLupBbOHTiCU0GPkMD6Do5UIueSLs5tUYOxYzjuPB5CFZughWSbBFlzeToDcwtubaR0B06ON5k0y8fIiPC+X+iYAdnq8eiGMWy2Msl20RPO1UMolg6hMScc0SYHYK6hDdOASbL1D5Uhy/oILDZvw4kbYXCrHkQlm6gF2YhonQgLDeP5QSjXB6UXuMfWa/X1ddzsL7DwMQ3ZZJD3ZCLefDv0ln+Jrdp2sEiqR3JjDQpjHOGuvgb7Vm/BTpsYeLX1oaE+HhHH1mP/F99g6wkXWKW3I3eAqZdTd5spFhLZFHI5TxHg6uLKzfqU04Nyc8RGx/A8KgKLB9OQrQ/S5jhEWWyH9vffQ/WgDU6HFiC2MBsPQ23hpLkee9fuwI5zIXArqkdZUQACjDZCfcUPUDnqhLOxDciWTGDkBbeHFgrZZFIpjyMjZ2HKQkWZsK5eucKPUVIjgcWFacg2AkVfJSqTAhDh4QG/8HTcL2lGVXM9GsrSkB3ugyCvIAQkliK3uQvtrUUoifdFsBvrG5WNxMoeNA0uTjWSXNPuJyTgpIkpT/1Ge2hOjk7c2vhH0Q4CCxvTkI2JpAk55LLJWtvDUhlk8jEoxsj3UYZR6TDPiDsik2OUJ3oZhVz6pO8opPJxKMaf8pmcIeYz2cjvk9INUNYtShP30/oNPPeHn7cPah7XLNo0bgIzMJC8CcxXshGRaKOasllRkh1KZEpuV5RYh/wehVl/cUOQbY5A0RCUgpy89Smh6Q61bdzySLkmKb+lCOgUmBOyTeYKnDuPh/lGNvJdpPTifr5+PKvVnl27cP7sWb5mo6Q8FGktIPBSZKPZmlyLKMc8ZQOeK8LNJ7KRsYOezd/Pn0uynWrbcdLkJM9SPND/x3lWBBYfZk02MnoMMKJRLpGQoGCkJCXPWazVfCEbrcEqK6t4nn4qQMELUxidQHRkFHp6RICnwK8xa7JRGuyy0hK4u7rxlNY3HK7zFNlzgflCNsrD6HFnsiDGnl27eQGJ6Kgont5cxJ4JPItZkY0GEhVyCPD35xmevl2xAvp6ejyaeC5yYswHslGq79DgYO7fqLZtG3cmTklJ5oUBBdEEfg+zIhsRirwgqBzQ11/+E+++9TaviEKZixvZ+u1loexkozwhEeER0NPR4ZmuTpqaMqKl8GIXAgJ/hBcmG83aZAwJDgzkAY9U1+udt97Ct9+sgPahQ7h/P+GlN26VmWwUi0ZWRvJzpAJ/lFKOClkIP0eB6fDCZCPrI+WWP3vGAqv+9QOWvrsEy5a8h4/e/4DX+aLCgVQNhcoHzRbKSrbBwSHExMTwNSpJcrI+kqcIpQMXqqPAdHghspH1jUoSXbG1w08/rscHS5fx9vEHH/KqlUQ4rQMHEMlUrJcxEigj2Si3ZmpKKowYwcgFizxDKAcmEU1AYCZ4IbKRVEtgKhOtVb76/Au884+3OME++/hjvP/eUi7hfvj2O56KrSC/YNbGEmUjG+2lUWlhqsapprqN+zzSmk1INIEXwYzJRhvW5GAbHhrK1CdDrF/3I1Z+vQLf/HM5Pv/kU/5KBcypXBEVdKeqlcOz3HdTJrINDQ9zT32S5pSVmLz3Q4ND5mybQ2DxYMZkIylF9afTUlN5oprLly7hmIEBr8288uuvsXWLCi5fvIibN27Ay8uL50GkooazmfmVhWyUvbmQfQ4He3vs27OXJ+a57XSLe8wICLwoZkw2Wq9RHWjyXqdqKZQG29fXB8YnTvCyRcePGnDDCSWtoVz+ZCQhj5LZuCspA9lo057Wp27svWkdqr57D67Y2KKooFB47wvMCjMmG5GGTPo0CKlwPO01UT03KitLA/HiBWtOMBqIpD7SOof+nq+Sra6uftIN67A2d8OytrqAnOxHPH5PQGA2eCEDydNQsDUcxW65u7nxlGzXrl7lBJwLvGmykQQPD4/AMSatqaInGUYy0tN5gUEBgdli1mQjKVfJVEYiwkFNLU62/r7+qbMvhzdJNvLUT0lOgfkZC+7vSCb+mOhoRrTBqR4CArPDrMlG67HS4mLcvnULmhoHcMXODr1z5On+psg2zqQ1GXYuWFphp9oOHNXV4/XRaM9QQOBl8XJkKylZUGQj4w/VQKM1qPquPXBzcUV9Xd3UWQGBl4Mg2xQoG5a/nx809u3Dnp27cNn6EvJy80SCHoE5gyAbA30W2oTX19PnheHPnjFHWmranK1BBQQIgmwMZaWluGhtzWtWU1YsStLDfR6FJ5bAHGLRk422K/x8fPleGm1e+/n6op6t3UTuEIG5xqImG63T0tPSeDHCvbt289QONTUikarAq8GiJdvY2Dh7/lLYXr6Mg5qauGhljcyMTF4RVEDgVWBRko3cyJqam7n6SNZHWqdRgUJhEBF4lViUZKPwmPCwcJgaG7Nn14DL7du8UKGAwKvEoiMb5brMYOs0irkjd6yLFy6gsKBgTjM6Cwj8HhYV2Uam6qXZX73K66WRT2dcbCyPWxMQeNVYVGSrra3l9yLVkayPtxxvzknqPQGBmWDRkG1goB8J8fE4bmDAUzdQnpSS4pI5SSorIDATLAqyKRRyFBYWwM7Wlvs90uZ1aGio2E8TeK1YFGSjCPK7dzwYyTShob6P5xQpLy+fOisg8Hqw4MlGaRzIS8TEyJhnxzp9ijJ/pQujiMBrx4InW3VVNXfD2rdXnauPVIK3s1PsqQm8fixoslHSoZDgEGgfPMSeUQPXrlxBQX4+W6sJlyyB14+XJ5sTI9t+DdjZEtl6ps6+HOaCbGRlpIRElOJg+1Y1nDEzQ3ISVQPtF1mMBd4IXopslB/y1k0nbnSwtbFVKrK1tbXxyGs9HV3o6+jhnq8fryknIPCm8NJkeyLZKD03lVOaC8wF2bIyM3HS9CQvKO986zZKiooxKhOmfoE3h1mTjRK1UvZjT4+7PL8iSThlyBtJQZ9Ees+7d6G+dy/OmpsjNyeHx64JCLxJzJps8tFRtDQ383WQh/sdXhBwrszpL0O2JwGh586e5dV2/H190d3VNXVWQODNYdZkm2ASRCaV8uzBzYx0XRLJnHnOvwzZGhsacO3KVa4+Ojk6oqS4WLhkCSgFZk22V4nZkI0sjLSBTWnCjxzW5mQjCUeSTlgfBZQBzyfbxDgmFDLIRoYYAYYxIlNAPs7WRZjA+JgcCpmUGx0U7NhcDufZkI321GgN6e7qhsNaB3HJ+iIamJQTEFAWPJ9s8h5IGx4iN9wdPu5e8L9fjKw2OSRsYPe3VqIqKRrJkfFILW9BHdPU5ir8cjZkI3U24F4ADA2O4fTJU0iIS+D3ERBQFkxDtm6MVEThgY0mTqrvgNY5b9hl9CK/SwpJxUMUuFzC3Uu2uJlcgVQZky5cvr18CrgXJRuvpVZcAstz57F/rzo87txBR3uHiL4WUCpMo0YqMNZVgVofQ9zWXoddR+1w5F4dYmtG0P24CM2Bjoi46YDbD0sR3TeBzr5hTFB2qpdcI70I2RRyBepq6xAcGAyj44YwNjqBdLZuE3kfBZQN0xtIFIOQZV1F8gVVaOhaYvf1bATkd0BSX4XOpBAk+3ogNCMRoeXVSM5tQkPTAFvXvT6ykddKfFw8zluc40Tz9vJGS2vr1FkBAeXB9GSDAqj3Qendw9A1OIedZ8PgkVCAmuoy1OZmIj0iDNn37yAsJhjXA0uRWDKI4ZfU3mZKNlITK8rL4XTjJrQPHYbN5csoKysTQaECSokZkI0xpzsSFREmOH78DHbo3YK9RzSy8gpQXF6FR8nJqAqzQ5SXI84HlCOsfBRDL6nBzYRspCZSPv7YmFicNbeAvq4e7vn7izg1AaXFzCSbNBGVSRYwPW4MlZ0XYG7tj9j0QpS3tqOqKBePfW0R5e4E+4cteNA1AdlL7gPMhGzkm0l9rjuwPqYnecYsSkknIKCsmJlkG8/A44dWMD9mAFVVS5hdiEBCbj3aRwbQUp2PXJerCHTzwL26PpSyK17WNDETsrW3d8DH24eX4aWa1wnxCeiZo6gDAYFXgRmQjaiTh/o8B1w5dZqtjW7immcu8psGIZ0YQXtFNh7cvAYvF2/EN/WjifV+2Q3u3yNbzTNkK+Vlni7yCOzLFy+hqrJKWCAFlBozJFsDupuSkBQejcDAbGSUSCCREqXk6G+pQVHSA2SkZaO6axgD7OirJltXVxfCw8O5qf/wwUPcEVrSKZk6KyCgnJgB2Rh1mARTjPZhsH8Qff2jGBmdwBPr/rhCDtnwCN9YVjDJ8rJEI0xHtszMTFywugDdIzqwOm+JlJQUEUIjoPSYAdkIc0GhmeN5ZCMPfm8vL+zbs5c7HPt4efOsxsJbREDZMUOyvV48SzY3V1fuVEyEqn5czU39lNWYrJDp6RncCVlAQNmh3GRzcIAZIxv5Ora0tLC1moSX4aVkq5SKgUhYV1c3dZWAgHJDKck2+BTZKKkqka2xsQEFBXkwMjTkheatrax47NqQWKsJzBMoNdkcmRppfvo0XJyd2f/Z8PXxgdrWrdDS0EBYSAhPK04R4wLKARGk+3woJ9mYtMrJyeFpDc5ZWMCBSTgvT09YnDkDNdWtsDx7FkVFRcIHUskg9jmfD6Um262bN2F1/jwuXLgAo+PHob5nL/eBDAoI5H6RAsqFcSbZyDeV9kHJm0dG4VYCP0M5DSSMbJR+jshGks3khDE2bfgJW1VU4eTkxCvQCAuk8oGUyJqaGkRHRSEyIhJFBYVzlt5wIUApyTbM1mx5ubm4ydRIKjJ/SOsg/v3d9ziwfz9SkpP5BrqAciI1JQWGx47j0AFNnuUsIyMDnR2dfHJc7Gs65SQbU0WIbFRHjYpi7FDbji0bN8Hm0iWeNk9AeZGYmMjX1V988il+XLMWxkwrueN+Bw8Z6drb26d6LU4oJdkofIbIdsXWFtuY6rhm1Wrs2bWbpzonw0inpBMdHR3cGtnS3ML34ER7s00ikfDfJJCtp7eqqOD9Je/hnf97G19+/gV+2rABJ01NERQYiLKSUt6XtJPFJumUkmyU/LUwvwBXbGyxfu06fP7pZ/iRvVKacytLS17Ew9bGhkm6y7gs2htvFCFvx36TSxcv8Xydq/71Az56/wMsefsdLGWk+/Tjj/HD9//Czu3bceK4IXccp4j6xbYcUEqyKeRyNDY0Ijw0jP84Kpu3YPfOXdDV0eE/JvlE/tLof9HeXJtMiEuN1taqW1Tw7Tcr8DlTIz/58CN8uOx9LH3nXbz993/gg6XL8ON/1/Gcnvn5+YvOyKWUZKPsXKOjcq6eJD5IhJuLG2uu8Pb2huddT3h6TDX6WzSlaL7ePvz19CkzrP3PGnzMJNuyJUs4wT5ihPv8k0+wft06fj4hLh6dTOUUaqQSgX6Mnu4eVFc/RmV5BS/ZS0Gioilfq69vQG1tLSPcXfy0fj3e+tvf8fe//hXLv/qKG0xo+8bF+TbSUlP5Wpu0l8UGpSYbYXycpNwo3yClRnq+aMrU6DeR8d+JojLi42KZyr8Tn338Cb5buRJHtLXh6uyMzIeZvOoROZkrFIqpX3dxQenJJjC/QEUoqaQypRakwN7wsDBUVlRgoH9A7LNNvQoIzAlIpQwOCkZoaCjy8/K5W50o2TUJQbZFAHIQljFV/HUM+u6ubtTW1PJ1mXCp+zUE2V45Jvh6ZpyyNrwhLYrKHpeUlKKUNSLDq0whMaYY46QWEQC/hSDbq8SEFBOKAQwOyTAwNAE52QXeAOHIcfuKnR2v8kMZpJuamkXOljcAQbZXhbFRKDqrIanIQlFlE0rbx9DLtKo3YSOgbGQUdLv8y69goH8UXp5ePISJ/EzJNU7g9UCQ7RVhXNaDztRgpN22hUdkGsIa5GiWsuNT518nyEK4eeNG/P0vf8U3y7/m4UoGevpwc3HhoUyDA5TtU+BVQ5DtlWAcipE2lIa4w+/MaTiHPEB8pwId8kktkkKIaqqrkZKcgqjISMRGx/CyV/FxcXPW7scn4H7CZLvhcJ17b3BfxXeX8NcvP/sc21W3cjM9pQMkQra2tAjL4SuEINsrwRBkQ1VIC/GHs7ULolKL0DQ2AcWUCtne2oLQ4Mnijdu3qWHvrt08WxjF681V09Q4AK2pRpETK5hEI+dgcqP6cOky7rNI/osrln+DrVtUccHSEpkZGaIK0CuEINucgwwPjRjpSkCY5x2ctwhFdFo9T8v+BJKODiZ54rmX/PGjBjA2MuIp+ygP5lw1ykpGyZJIch3U1ML3K1bio2WMbB98iGVL3sPb//g/LHnrHSz/4iteGvm2kxMqysqEZHuFEGSbc9BgrYW0Kwqxwf64ap+BxBwJnk64Jx0ZQWNDA3Jyc3lkc3paGg+unMuWlZXF12M5jx7B+dZtHhP4tz//hauR5I1Pkm7zxk0wMTSCn48PL1QipNqrhSDbnIMkmwSK4VJUlhYhLaMZNc0jeDoPGO1BkV9hf38/T4xD+2B9c9wGBga4pXGIEYjM/T+t34C//M+f8cWnn3G10mwqH2daSioa6uoE0V4DBNnmHLQwG8XE2CCGhwbRS4VIZHNTcGS2yM3J5XFnJN30jujiltMtLk3J9E+OwWID+vVAkG0RoKy0DFaWVtwgQ5bHvLxckfXqtQP4/yNcvGw3kKA5AAAAAElFTkSuQmCC)
Related Questions to study
physics
As shown in figure a block of mass m is attached with a cart. If the coefficient of static friction between the surface of cart and block is µ than what would be accelcration a of cart to prevent the falling of block ?
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)
As shown in figure a block of mass m is attached with a cart. If the coefficient of static friction between the surface of cart and block is µ than what would be accelcration a of cart to prevent the falling of block ?
![](data:image/png;base64,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)
physicsGeneral
physics
A block B. placed on a horizontal surface is pulled with initial velocity V. If the coefficient of kinetic friction between surface and block is µ . than after bons much time, block will come to rest ?
A block B. placed on a horizontal surface is pulled with initial velocity V. If the coefficient of kinetic friction between surface and block is µ . than after bons much time, block will come to rest ?
physicsGeneral
physics
An impulsive force of 100 N acts on a body for 1 sec What is the change in its linear momentum ?
An impulsive force of 100 N acts on a body for 1 sec What is the change in its linear momentum ?
physicsGeneral
maths-
If
defined by ![f left parenthesis x right parenthesis equals fraction numerator e to the power of x squared end exponent minus e to the power of negative x squared end exponent over denominator e to the power of x squared end exponent plus e to the power of negative x squared end exponent end fraction text , then end text f text is end text](data:image/png;base64,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)
If
defined by ![f left parenthesis x right parenthesis equals fraction numerator e to the power of x squared end exponent minus e to the power of negative x squared end exponent over denominator e to the power of x squared end exponent plus e to the power of negative x squared end exponent end fraction text , then end text f text is end text](data:image/png;base64,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)
maths-General
maths-
is a function defined by ![f left parenthesis x right parenthesis equals fraction numerator e to the power of ∣ x end exponent minus e to the power of negative x end exponent over denominator e to the power of x plus e to the power of negative x end exponent end fraction. text Then end text f stack stack text is end text with _ below with _ below](data:image/png;base64,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)
is a function defined by ![f left parenthesis x right parenthesis equals fraction numerator e to the power of ∣ x end exponent minus e to the power of negative x end exponent over denominator e to the power of x plus e to the power of negative x end exponent end fraction. text Then end text f stack stack text is end text with _ below with _ below](data:image/png;base64,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)
maths-General
physics
The force acting on a body whose linear momentum changes by 20 kgms-1 in 10sec is
The force acting on a body whose linear momentum changes by 20 kgms-1 in 10sec is
physicsGeneral
physics
Average force exerted by the bat is
Average force exerted by the bat is
physicsGeneral
physics
A cricket ball of mass 150 g. is moving with a velocity of 12m/s and is hit by a bat so that the ball is turned back with a velocity of 20 m/s If duration of contact between the ball and the bat is 0.01sec The impulse of the force is
A cricket ball of mass 150 g. is moving with a velocity of 12m/s and is hit by a bat so that the ball is turned back with a velocity of 20 m/s If duration of contact between the ball and the bat is 0.01sec The impulse of the force is
physicsGeneral
physics
Assertion : It is difficult to move bike with its breaks on.
Reason : Rolling friction is converted into sliding friction, which is comparatively larger.
Assertion : It is difficult to move bike with its breaks on.
Reason : Rolling friction is converted into sliding friction, which is comparatively larger.
physicsGeneral
physics
Assertion : A body falling freely under gravity becomes weightless.
Reason:![straight R equals straight m left parenthesis straight g minus straight a right parenthesis equals straight m left parenthesis straight g minus straight g right parenthesis equals 0](data:image/png;base64,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)
Assertion : A body falling freely under gravity becomes weightless.
Reason:![straight R equals straight m left parenthesis straight g minus straight a right parenthesis equals straight m left parenthesis straight g minus straight g right parenthesis equals 0](data:image/png;base64,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)
physicsGeneral
physics
Assertion : body of trans 1 k 6 is moving with an acceleration of The rate of change of its momentum is 1 N
Reason : The rate of change of momentum of body = force applied on the body.
Assertion : body of trans 1 k 6 is moving with an acceleration of The rate of change of its momentum is 1 N
Reason : The rate of change of momentum of body = force applied on the body.
physicsGeneral
physics
Assertion : Frictional forces are conservative forces.
Reason: Polential energy can be associated with frictional forces
Assertion : Frictional forces are conservative forces.
Reason: Polential energy can be associated with frictional forces
physicsGeneral
physics
When forces F1,F2,F3 are acting on a particle of mass m such that F2 and F3 are mulually perpendicelar. then the particle remains stationary. If the force F1 is now removed than the acceleration of the particle is
When forces F1,F2,F3 are acting on a particle of mass m such that F2 and F3 are mulually perpendicelar. then the particle remains stationary. If the force F1 is now removed than the acceleration of the particle is
physicsGeneral
physics
The minimum force required to start pushing a body up a rough (coefficient of ) inclined plane is F1. While the minimum force needed to prevent it from sliding down is F2. If the inclined plane makes an angle
from the horizontal. such that than
the ratio
is
The minimum force required to start pushing a body up a rough (coefficient of ) inclined plane is F1. While the minimum force needed to prevent it from sliding down is F2. If the inclined plane makes an angle
from the horizontal. such that than
the ratio
is
physicsGeneral
physics
A mass of 6 kg is suspended by a rope of length 2 m form the ceiling . A force of 50 N in the horizental direction is applied at the mid Point P of the rope as shown in figure. what is the angle the rope makes. with the vertical in equilibrium ? (g=10 ms2) Neglect mass of the rope:
![](data:image/png;base64,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)
A mass of 6 kg is suspended by a rope of length 2 m form the ceiling . A force of 50 N in the horizental direction is applied at the mid Point P of the rope as shown in figure. what is the angle the rope makes. with the vertical in equilibrium ? (g=10 ms2) Neglect mass of the rope:
![](data:image/png;base64,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)
physicsGeneral