Physics Homework: Solving Problems on Uniform Motion

This assignment provides detailed solutions to five physics problems related to linear motion. The problems cover concepts such as uniform acceleration, calculating the length of a water slide given initial conditions and final velocity, determining average acceleration of a rugby player, calculating the displacement of a motorcycle racer undergoing deceleration due to friction, determining the time it takes for a car to stop given initial speed and deceleration, and calculating the final velocity of a high diver falling from a platform. Each solution includes the relevant formulas, variable substitutions, and the final answer, demonstrating a clear understanding of kinematic principles. This resource is beneficial for students seeking to understand and solve motion-related problems.

Question 1
A fun seeker begins sliding from the top of a water slide and accelerates uniformly at 0.86 m.
s-2. If they reach a velocity of 7.78 m.s-1 at the bottom of the slide, what length must the
slide be? If rounding is required, please express your answer to two decimal places.
Solution
a=0.86 , v =7.78 ,u=0
From equations of uniform linear motion
v2=u2 +2 as
Substituting the variables,
7.782=02+(2 ×0.86 × s)
length of slide s= 60.5284
1.72 =35.1909
Question 2
If a rugby player is running at 2.82 m/s and then decides to sprint in a straight line for a ball
and 2.38 seconds later is running at 7.8 m/s, what is their average acceleration during that
time?
Solution
From linear motion equations,
a= v−u
t =7.8−2.82
2.38 =2.0924
Question 3
A motorcycle racer falls off their motorbike while traveling at 112 km/hr and skids in a
straight line down the track. If the friction with the track decelerates the rider at a uniform
rate of 4.4 m/s/s, how far (what displacement) would the rider travel before coming to a stop?
Solution
v=0 , u= 112 km
hr (converting speed into m/s)=112 ×1000
60 ×60 =31.111 m/s
a=−4 m s−2
From equations of linear motion,
v2=u2 +2 as
o=31.1112 +(2 ×−4 × s)
s=−967.90
−8 =120.9877

Question 4
An out of control car traveling at 60 km/hr locks its brakes and skids in a straight line. If the
friction caused by locking the brakes decelerates the car at a uniform rate of 2 m/s/s, how
long (what time) will it take for the car to come to rest?
Solution
u=60 km
hr = 60 ×1000
60 ×60 =16.6667
v=0
a=−2
From linear motion question,
v=u+at
t= v−u
a =a=0−16.6667
−2 =8 1
2
Question 5
A high-diver performs a handstand dive (falls vertically) from a 38 m platform. What
velocity will the diver hit the water with if they fall from this height? Tip: Remember that any
motion downwards is negative (-ve). Please indicate the direction of this velocity accordingly
in your answer for this question.
Solution
a=g=9.80
u=o
v=?
s=38m
v2=u2 +2 as
v= √ u2+2 as= √ 2∗9.8∗38=−27.29