Question

(4.1) A motorcycle and a minivan are at rest, side by side, at a stoplight. 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 (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 (i) at t = 1 s,
(ii) at t = 5 s,
(iii) at t = 10 s and
(iv) at t = 12 s
(c) Determine the displacement of the motorcycle (i) at t = 1 s,
(ii) at t = 5 s,
(iii) at t = 10 s, and
(iv) at t = 12 s.
(d) Determine the displacement of the minivan (i) at t = 1 s,
(ii) at t = 5 s,
(iii) at t = 10 s, and
(iv) at t = 12 s.

Answer 1

Ans:

a) For motorcycle:

Given u=0, a=4m/s² for t=0 to 5s, a=0 m/s2 from t=5s

From kinematics,

Here v is the spedd at time t

i: at t=1s => v = 4x1 = 4 m/s

ii: at t =5s => v = 4 x 5 =20 m/s, this is the final velocity after acceleration and the vehicle will continue with this velocity.

iii: at t=10 => v = 20 m/s

iv: at t=12s => v = 20 m/s

b) For minivan:

Given u=0, a=2m/s² for t=0 to 10s

From kinematics,

Here v is the spedd at time t

   i: at t=1s => v = 2x1 = 2 m/s

ii: at t =5s => v = 2 x 5 =10 m/s

iii: at t=10 => v = 2 x 10 =20 m/s, this is the final velocity after acceleration and the vehicle will continue with this velocity.

iv: at t=12s => v = 20 m/s

c) For motorcycle:

Given u=0, a=4m/s² for t=0 to 5s, a=0 m/s2 from t=5s

From kinematics,

Here s_o is the initIal position, u is the initial velocity, t is the time taken.

i: at t=1s => s = 2x1^2 = 2 m

ii: at t =5s => s = 2 x 5^2 = 50 m

iii: at t=10 => s = 50 m+20 x(10-5)+0 = 150 m

iv: at t=12s => s = 50 m +20 x (12-5) +0 = 190 m

d) For minivan:

Given u=0, a=2m/s² for t=0 to 10s, a=0 m/s2 from t=10s

From kinematics,

i: at t=1s => s = 1x1^2 = 1 m

ii: at t =5s => s = 1 x 5^2 = 25 m

iii: at t=10 => s = 1 x10^2 = 100 m

iv: at t=12s => s = 100 m +20 x (12-10) +0 = 140 m