Answer to Question #239821 in Physics for Tin

Question

A racecar starts from rest and travels east along a straight and level track. For the first 5.0 s of the car’s motion, the eastward component of the car’s velocity is given by 𝑣(𝑡) = (10.860𝑚/𝑠 3 )𝑡 2 . What is the acceleration of the car when 𝑣𝑥 = 12.0𝑚/𝑠?

Answer 1

Given:

$v(t)=10.860t^2\:\rm m/s$

The acceleration

$$a(t)=v'(t)=21.72t$$

The velocity of racecar is equal $v=12.0\:\rm m/s$ for the time $t=\sqrt{12.0/10.86}=1.051\:\rm s$. At this instant it acceleration

$$a=21.72*1.051=22.83\:\rm m/s^2$$