The speed-time graph of two cars A and B appr | vedclass

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Question

(B) The slope of the $v-t$ graph gives the acceleration or retardation. For both cars,the magnitude of acceleration is $|a| = \frac{20\,m/s}{4\,s} = 5

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(B) The slope of the $v-t$ graph gives the acceleration or retardation. For both cars,the magnitude of acceleration is $|a| = \frac{20\,m/s}{4\,s} = 5\,m/s^2$.Car $A$ starts from rest and accelerates,so its displacement at time $t$ is $s_A = \frac{1}{2} 	imes 5 	imes t^2$.Car $B$ starts with an initial velocity of $20\,m/s$ and undergoes retardation,so its displacement at time $t$ is $s_B = 20t - \frac{1}{2} 	imes 5 	imes t^2$.The cars will cross each other when the sum of their displacements equals the initial distance between them:$s_A + s_B = 60$$\frac{1}{2} 	imes 5 	imes t^2 + (20t - \frac{1}{2} 	imes 5 	imes t^2) = 60$$20t = 60$$t = 3\,s$.

The speed-time graph of two cars $A$ and $B$ approaching each other is shown in the figure. The initial distance between them is $60\,m$. The two cars will cross each other after time $..........\,s$.

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