A body A moves with a uniform acceleration a and zero initial velocity. Another body B, starts from the same point moves in the same direction with a constant velocity v. The two bodies meet after a time t. The value of t is

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Solution

For body A,
Distance travelled in t seconds with initial velocity zero and acceleration a,
$s = u t + \frac{1}{2} a t^{2} = 0 + \frac{1}{2} a t^{2}$

For body B,
Distance travelled in time t with unifrom velocity v, s = vt
Since distance travelled is same for both the bodies when they meet,
$v t = \frac{1}{2} a t^{2}$
$∴ t = \frac{2 v}{a}$

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A body A moves with a uniform acceleration a and zero initial velocity. Another body B, starts from the same point moves in the same direction with a constant velocity v. The two bodies meet after a time t. The value of t is

For body A,Distance travelled in t seconds with initial velocity zero and acceleration a,s=ut+12at2=0+12at2For body B, Distance travelled in time t with unifrom velocity v, s = vtSince distance travelled is same for both the bodies when they meet, vt=12at2∴t=2va