Applied Physics (XXXXX)
College of Technology (COLTECH)
Semester: First Semester
Level: 200
Year: 2016
THE UNIVERSITY OF BAMENDA
COLTECH
Applied Physics
Tutorial Sheet 1
1) An animal is positioned some 20m from a reference point. At time t=0s, it rushes forward towards
a target located 30m ahead. The animal’s motion during the first 2s is described by the equation: x
= 20 + 5t
2
, where t is time. Find:
a) The displacement of the animal in the time interval t=1s and t=2s.
b) The average velocity in this time interval.
c) The instantaneous velocity at times t=1s and t=2s.
Derive an expression for the instantaneous velocity with time.
2) Suppose the velocity of a car moving along a straight path is described as a function of time by the
v = a + bt
2
where a and b are constants. If a=10m/s and b=2m/s, find:
a) The change in velocity of the car in the interval t=2s and t=5s.
b) The average acceleration in this time interval.
c) The instantaneous acceleration at times t=2s and t=4s.
Derive an expression for the instantaneous acceleration with time.
3) A motorcyclist crosses a police checkpoint and accelerates at a constant rate of 4m/s
2
. If velocity
is 3m/s, 5m from the checkpoint:
a) Find the position and velocity of the motorist after 2s.
b) What is the position when the velocity is 5m/s?
4) A car travelling along a straight accelerates at a rate of a = m – nt. If its velocity at the origin is v
0
:
a) Derive expressions for the velocity and position as functions of time.
b) At what time is the velocity at its greatest?
c) What is this maximum velocity?
5) A boy standing on the first floor of a building throws a ball vertically upwards such that it drops to
the ground. If the ball leaves the boy’s hand at 15m/s, find:
a) The position and velocity of the ball after 1s and 5s.
b) The maximum height and the time it takes to reach it.
c) The velocity when the ball is 5m from the boy’s hand
Sketch graphs of the displacement and velocity with time.
6) The acceleration of a motorcycle starting from rest at time t=0 is given by a = 1.2t – 0.12t
2
. Find
its position and velocity as functions of time. Calculate the maximum velocity.
7) The motion of a particle along a straight path is described by the function x = 6 + 5t
2
– t
4
.
a) Find the position, velocity and acceleration at time t=2s
b) During what interval of time is the velocity positive and what is the maximum velocity?
c) During what interval of time is x positive?
(Take t to be positive)
8) A 150-meter long “moving sidewalk” in an airport terminal building moves at 1m/s. if a man steps
on it at one end walks at 2m/s relative to the moving sidewalk, how much time does he require to
reach the opposite end if he walks in the
a) Same direction as the sidewalk
b) Opposite direction
9) The coordinates of a particle moving in the x-y plane as a function of time are given by x = 1 + 2t
2
and y = 2t + t
3
. Find the position, velocity and acceleration of the particle at time t=2s.
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10) A motorcyclist rides off the edge of a cliff with the horizontal velocity of 5m/s. Find his position
and velocity after 0.5s.
11) A boy shoots an arrow from ground level at an apple hanging in a tree. At the same time he
releases the arrow, the apple falls from the tree and drops straight down. Show that the arrow’s
path curves just enough for it to hit the apple, regardless of its initial velocity.
12) From a projectile launched with speed v
0
at initial angle θ
0
, derive general expressions for the
maximum height, h and range, R of the projectile. What value of θ
0
gives the maximum range for
a given v
0
? If a footballer wants to throw a football at 20m/s to a receiver 30m away, at what angle
should he throw the ball?
13) A man stands on the roof of a 50m tall building and throws a stone with a velocity of 60m/s art an
angle 37ﹾ above the horizontal. Calculate:
a) The maximum height above the roof the stone reaches
b) The magnitude of the resultant velocity of the stone just before is strikes the ground
c) The horizontal distance from the base of the building to the point where the stone strikes the
ground.
14) What is the acceleration of a car travelling at a constant speed of 20m/s round a curve of radius
100? If an object travels in a circular path of radius 50m at a period of 4s, what is its acceleration?
15) A body slides along a horizontal path such that its position as a function of time is described by
the equation: x = 18t
2
– 3t
3
. Derive an expression for the force acting on the body and the
magnitude of this force at time t=5s. When is the force positive?
16) It takes a force of 400N acting at 60ﹾ to the horizontal to set a 50kg mass in motion on a rough
horizontal surface. However, once set into motion the mass can be kept in motion by a constant
horizontal force of 100N. What are the coefficients of static and kinetic friction? What is the
friction force on the mass if it is unmoved by a horizontal force of 75N?
17) A gymnast has just begun climbing a rope hanging from a gymnasium ceiling. She stops
suspended from the lower end of the rope by her hands. If her mass is 60kg and that of the rope is
10kg, analyse the forces on the gymnast and the rope.
18) An object of weight w hangs from a cord knotted at a point to two others; one fastened to the
ceiling and the other to the wall. Assuming that the weights on the cords are negligible, find the
tensions in the three cords. (Take the mass of the object to be 5kg).
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