A body 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

Question

A body 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 (A)  (2v/a)  (B)  (v/a)  (C)  (v/2a)  (D)  √(v/2a)

Tardigrade Admin · Accepted Answer

sA=u t+(1/2) a t2 or sA=0+(1/2) a t2=(1/2) a t2 sB=v t Given, sA=sB ∴ (1/2) a t2=v t or t=(2 v/a)

Q. A body 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

$\frac{2 v}{a}$

$\frac{v}{a}$

$\frac{v}{2 a}$

$\frac{v}{2 a}$

$s_{A} = u t + \frac{1}{2} a t^{2}$
or $s_{A} = 0 + \frac{1}{2} a t^{2} = \frac{1}{2} a t^{2}$
$s_{B} = v t$
Given, $s_{A} = s_{B}$
$∴ \frac{1}{2} a t^{2} = v t$
or $t = \frac{2 v}{a}$

Q. A body 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

a2v​

av​

2av​

2av​​

sA​=ut+21​at2 or sA​=0+21​at2=21​at2 sB​=vt Given, sA​=sB​ ∴21​at2=vt or t=a2v​

Q. A body 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

$\frac{2 v}{a}$

$\frac{v}{a}$

$\frac{v}{2 a}$

$\frac{v}{2 a}$

$s_{A} = u t + \frac{1}{2} a t^{2}$
or $s_{A} = 0 + \frac{1}{2} a t^{2} = \frac{1}{2} a t^{2}$
$s_{B} = v t$
Given, $s_{A} = s_{B}$
$∴ \frac{1}{2} a t^{2} = v t$
or $t = \frac{2 v}{a}$