# Math Help - velocity, time, displacement question

1. ## velocity, time, displacement question

Could someone check this because I have different answers to those given for parts iib amd iii.

2. ## Re: velocity, time, displacement question

(i) is correct, but I think you have misunderstood the others. In (ii)(a), you have correctly calculated that this is 2/3 of the answer to (i) but remember that (i) gave the least distance in which it is possible to do what is asked. Since the distance in (ii)(a) is less than that, this is impossible. You simply cannot accelerate to V and then decelerate to a stop within that distance. For (ii) (b) you have, again correctly, calculated that this is 4/3 of the answer to (i). Since that is larger than (i) this is possible. But you seem to have assumed that the car would still accelerate and decelerate at the given values during that entire time. Since V is the maximum speed the car must accelerate at a for time $t_1$, which equals $\frac{V}{a}$ as you show, then drive some unknown time, t, at constant speed V, then decelerate for time $t_2= \frac{V}{r}$. Find the total distance in terms of V, a, r, and t and set it equal to the given distance to solve for t. The total time required will be $t_1+ t_2+ t$.