Physics
04.01.2021 12:24
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At a certain instant of time, a toy car is traveling at a constant speed of v0 to

At a certain instant of time, a toy car is traveling at a constant speed of v0 to the right, while a distance d ahead is another toy car starting from rest and traveling to the left with constant acceleration a. the cars are moving along the same line, directly toward each other. at what time do they collide, in terms of d, v0 and a?
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sofiisabella10
sofiisabella10
4,7(46 marks)

They collide after t=\frac{-2u+\sqrt{4u^{2}+8aD}}{2a}

Explanation:

The time in which the two cars collide will be equal to the time in which they two cover the distance 'D'.

Let the cars meet after 't' time

Distance covered by toy car travelling at a constant velocity equals

D_{1}=v_{0}t................(i)

Distance that the accelerating car travles in the same time 't' can be obtained from second equation of kinematics as

D_{2}=ut+\frac{1}{2}at^{2}\\\\D_{2}=\frac{1}{2}at^{2}(\because u=0)

Now the condition dictates that

D_{1}+D_{2}=D\\\\\therefore ut+\frac{1}{2}at^{2}=D

Solving the quadratic equation for 't' we get

at^{2}+2ut-2D=0\\\\\therefore t=\frac{-2u+\sqrt{4u^{2}+8aD}}{2a}

We neglect negative value since time cannot be negative.

rileybantaos1c8s
rileybantaos1c8s
4,6(21 marks)

b) determine if the area is safe

Explanation:

none of the other things she does will matter if the area's not safe, so that should be the first thing she does. i hope this helps! :)

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