Question

1. 1-D Kinematiics, Variable Acceleration An object, at rest at t = 0, is subject to a time dependent acceleration in the z direction of the form a(t) = ao exp-bt Calculate v(t) and a(t) 2. 1-D Kinematics, Constant Acceleration After falling a distance of 45.0 m from the top of a building, a box is landing on the top of a car, which is crushed to a depth of 0.50 m due to the impact. g-9.8m/s2 a) the speed of the box just before it touches the top of the car b) The average acceleration of the box during the impact c) The time it took to crush the roof 3. 2-D Kinematics An octopus swimming in a horizontal plane has the velocity (4.0+1.00ý)m/s at the time t-0. After the octopus swims for 10.0 s with a constant acceleration, its velocity is ขึ (20.0-5.00i)m/s. a) What are the components of the acceleration? b) What is the direction of the acceleration relative to the unit vector ?

Answer 1

a(t) = a_0 e^(-b t) Now, integral^v_0 V(t) = integral^t_0 a(t) dt = integral^t_0 a_0 e^(-10 t) dt = [a_0/-b e^-bt]^t_0 = (a_0/-b) [e^-bt - 1] Now integral^x_0 x(t) = integral^t_0 V(t) dt x = a_0/-b integral (e^-bt - 1) dt = a_0/-b [e^-bt/-b - t]^t_0 = a_0/-b [e^-bt/-b - t - 1/-b = a_0/-b [1 - e^-bt/b -t]