Answer to Question #180385 in Classical Mechanics for Robin

Question

1. a car accelerates with constant acceleration from a standstill to the speed v0 = 90km / h on a straight line for a period of time t1. the velocity from t = 0 to t = t1 is given by:

V(t)= v0(t/t1)^2

how big is the car's average speed during this time?

2, a particle moves at a constant speed u on a circular path. The period of the movement is t1. what is the amount of the particle's average acceleration from time t = 0 to t = (3/2)t1

Answer 1

1)

$s=\int_0^{t_1}v(t)dt=\frac{v}{t_1^2}\int_0^{t_1}t^2dt=\frac{v}{t_1^2}\cdot\frac{t_1^3}{3}=\frac{vt_1}{3},$

$v_{av}=\frac{s}{t_1}=\frac v3=30~\frac{km}{h}.$

2)

$a_{av}=\frac{u_2-u_1}{t_1}=\frac{u-u}{t_1}=0.$