Question

7.1) A motorcycle and a minivan are at rest, side by side, at a stoplight. A pickup truck is approaching the intersection, from behind the motorcycle and minivan, at 20 m/s. At the instant the traffic light turns green, t = 0 s, the pickup truck is 120 m behind the minivan. When the light turns green, the motorcycle accelerates at 4 m/s 2 for five seconds, while the minivan accelerates at 2 m/s 2 for ten seconds. Once each vehicle stops accelerating, it maintains a constant speed. (a) Determine the speed of the motorcycle from the perspective of a passenger in the truck (i) at t = 1 s, (ii) at t = 5 s, (iii) at t = 10 s, and (iv) at t = 12 s. (b) Determine the speed of the minivan from the perspective of a passenger in the truck (i) at t = 1 s, (ii) at t = 5 s, (iii) at t = 10 s and (iv) at t = 12 s (c) Determine the position of the motorcycle relative to a passenger in the truck (i) at t = 1 s, (ii) at t = 5 s, (iii) at t = 10 s, and (iv) at t = 12 s. (d) Determine the position of the minivan relative to a passenger in the truck (i) at t = 1 s, (ii) at t = 5 s, (iii) at t = 10 s, and (iv) at t = 12 s.

Answer 1

a)

V_t = velocity of truck relative to ground = 20 m/s

Consider the motion of motorcycle

V_mo = initial velocity of motorcycle = 0 m/s

a_m = acceleration = 4 m/s²

t = time of travel

V_m = velocity of motorcycle at any time "t" relative to ground

velocity of motorcycle at any time "t" is given as

V_m = V_mo + a_m t

V_m = 0+ 4t

V_m = 4t

velocity of motorcycle relative to truck is given as

V_mt = V_m - V_t

V_mt = 4t - 20

i)

at t = 1 s

V_mt = 4(1) - 20

V_mt = -16 m/s

ii)

at t = 5 sec

V_mt = 4(5) - 20

V_mt = 0 m/s

iii)

at t = 10 s

V_mt = 20 - 20

V_mt = 0 m/s

iv)

at t = 12 s

V_mt = 20 - 20

V_mt = 0 m/s

b)

V_t = velocity of truck relative to ground = 20 m/s

Consider the motion of van

V_vo = initial velocity of van = 0 m/s

a_v = acceleration = 2 m/s²

t = time of travel

V_v = velocity of van at any time "t" relative to ground

velocity of van at any time "t" is given as

V_v = V_vo + a_v t

V_v = 0+ 2t

V_v = 2t

velocity of van relative to truck is given as

V_vt = V_m - V_t

V_vt = 2t - 20

i)

at t = 1 s

V_vt = 2(1) - 20

V_mt = -18 m/s

ii)

at t = 5 sec

V_vt = 2(5) - 20

V_vt = - 10 m/s

iii)

at t = 10 s

V_vt = 2(10) - 20

V_vt = 0 m/s

iv)

at t = 12 s

V_vt = 20 - 20

V_vt = 0 m/s