Question

6. 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

The velocity of the car is given by

$$𝑣_x(𝑡) = (10.860\:{\rm m/s^3} )𝑡^2$$

$$𝑣_𝑥(t_1) = 12.0\:\rm m/s$$

$$12.0=10.860t_1^2$$

$$t_1=1.051\:\rm s$$

The acceleration

$$a_x(t)=v'(t)=21.72{\:\rm m/s^2}t$$

$$a_x(t_1)=21.72{\:\rm m/s^2}*1.051\: \rm s=22.83\: m/s^2$$