Find the position and velocity of an object moving along a straight line with the given acceleration, initial velocity, and initial position.

Question

a(t) = -32

v(0) = 70

s(0) = 10

Answer 1

Velocity is integral of acceleration, v = ∫(-32) dt = -32 t + C_v, and C_v = v(0) = 70.

Position is integral of velocity, s = ∫(-32 t + 70) dt = -16 t² + 70 t + C_s, and C_s = s(0) = 10.

Thus s(t) = -16 t² + 70 t + 10 and v(t) = -32 t + 70.