Question

A particle moves along the x-axis according to x(t)=10t−2t²m. (a) What is the instantaneous velocity at t = 2 s and t = 3 s? (b) What is the instantaneous speed at these times? (c) What is the average velocity between t = 2 s and t = 3 s?

Answer 1

a) v(2) = 2m/s, v(3) = -2m/s

b) speed at t = 2s is 2m/s

speed at t = 3s is 2m/s

c) 0 m/s

Step-by-step explanation:

We can take the derivative of x(t) to find the equation of velocity

v(t) = x'(t) = 10 - 4t

(a) v(2) = 10 - 4*2 = 10 - 8 = 2 m/s

v(3) = 10 - 4*3 = 10 - 12 = -2 m/s

(b) The speed would be the same as velocity without the direction

speed at t = 2s is 2m/s

speed at t = 3s is 2m/s

(c) The average velocity between t = 2s and t = 3s is distance it travels over period of time

`v_a = (s(3) - s(2))/(\Delta t) = (10*3 - 2*3^2 - (10*2 - 2*2^2))/(3 - 2)`

`v_a = (12 - 12)/(1) = 0/1 = 0 m/s`