Question

3. A race car's velocity during the first 5 seconds of a race can be modeled by v(t)7t 0.5t. Naturally, at t-o the position is zero (it's at the start line). a. Determine the equations for its displacement and acceleration. b. What is the displacement during these 5 seconds? c. What is the average velocity between seconds 4-5? d. Is the average speed the same as the average velocity in this situation?

Answer 1

V(t) = 7 t - 0.5 t^2 at t = 0, x_i = 0 t^2 v = d x/dt dx/dt = 7t - 0.5 t^2 integral_x_i^x_f dx = integral_0^t (7t - 0.5 t^2) dt x_f - x_i = 7 t^2/2 - 0.5 t^3/3 x_f = 7 t^2/2 - 0.5 t^3/3 rightarrow Equation for Displacement v(t) = 7t - 0.5 t^2 a = dv/dt = 7 - 0.5 times 2 t a = 7 - t rightarrow E2quation for acceleration displacement using first 5 second x = 7 t^2/2 - 0.5 t^3/3 x = 7/2 times 25 - 0.5/3 times 125 x = 87.5 - 20.83 x = 66.67 m Average velocity between 4 to 5 second v_avg = total displacement/time = x_5 - x_4/t x_5 = displacement in 5 second, m x_4 = displacement in 4 second, m x_4 = 7/7 times 16 - 0.5 times 64/3 = 56 - 10.66 x_4 = 45. 34 m v_avg^vector = 66.67 - 45.34/1 v_avg^vector = 21.33 m/s average speed and average velocity is same for time interval of