Answer to Question #180385 in Classical Mechanics for Robin

Question #180385
  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


1
Expert's answer
2021-04-13T06:30:20-0400

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."


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