Question

A rocket sled for testing equipment under large accelerations starts at rest and accelerates according to the expression a = (4.3 m/s 3 )t + (7.7 m/s 2 ). How far does the sled move in the time interval t = 0 to t = 2.4 s ? Answer in units of m.

Answer 1

v = $\small \int$ a dt
v = 2.15t² + 7.7t + v_o

AT t=0, v = 0+0+v_o = 0 => v_o = 0
v = 2.15t² + 7.7t

x = $\small \int_{0}^{2.4}$ v dt
x = (2.15 / 3)t³ + (7.7 / 2)t² (evaluate over 0 ≤ t ≤ 2.4)
x = 0.716(2.4)³ + 3.85(2.4)²
x = 32.0832 m