An automobile and a truck start from rest at the same instant, with the automobile initially at some distance behind the truck. The truck has a constant acceleration of `2.2 m//s^2` and the automobile has an acceleration of `3.5 m//s^2`. The automobile overtakes the truck when it (truck) has moved 60 m.
(a) How much time does it take the automobile to overtake the truck ?
(b) How far was the automobile behind the truck initially ?
(c) What is the speed of each during overtaking ?

Answer

A, B, C

Explanation

(a) For truck
`s_1=1/2 a_1t^2`
`60=1/2xx2.2xxt^2`
`:. t=7.39s`
(b) For automobile
`s_2=1/2a_2t^2=1/2xx3.5xx(7.39)^2`
`=95.5 m`
`:.` Initial distance between them,
`=s_2-s_1`
`=35.5 m `
(c) `v_1=a_1t=(2.2)(7.39)=16.2 m//s`
and `v_2=a_2t=(3.5)(7.39)=25.9 m//s`