Question
A sprinter takes a time of 11.0 s to run a 100 m race. She first accelerates uniformly from rest, reaching a speed of \(10ms^{-1}\). She then runs at a constant speed of \(10ms^{-1}\) until the finish line. What is the uniform acceleration of the sprinter for the first part of the race?
A \(0.5 m s^{–2}\) B \(0.91 m s^{–2}\) C \(1.7 m s^{–2}\) D \(5.0 m s^{–2}\)
Answer/Explanation
Ans: D
Let the time of acceleration be t, then we have the total distance traveled in the acceleration phase and the constant velocity phase, given as,
100 = (1/2)at^2 + 10( 11-t)
Also we have,
v = at therefore,
a = 10/t
substituting this in the above equation we get,
100 = (1/2)*( 10/t)*t^2 + 110 – 10t
100 = 5t – 10t + 110
t = 2 s
Hence the acceleration is therefore,
a = 10/2 = 5 m/s^2.
Question
An archer shoots an arrow at a target. The diagram shows the path of the arrow.
Air resistance is negligible.
The graphs show how three different quantities p, q and r vary with time.
Which quantity could be the horizontal component of displacement and which quantity could be
the vertical component of displacement of the arrow?
Answer/Explanation
Ans :B
The horizontal component of velocity remains constant, therefore the horizontal displacement varies uniformly with time, hence the graph q, which has positive constant slope represents the horizontal displacement.
The vertical displacement is given by the equation of motion under constant acceleration, which is the motion of a parabola,
y = ut + (1/2)at^2
hence the graph r represents that of the vertical displacement.
Question
Two cars X and Y are positioned as shown at time t = 0. They are travelling in the same direction. X is 50 m behind Y and has a constant velocity of 30 m s–1. Y has a constant velocity of 20 m s–1.
What is the value of t when X is level with Y?
A 1.0 s B 1.7 s C 2.5 s D 5.0 s
Answer/Explanation
Ans: D
Let the car X come to level with Y in time t seconds, then the difference in the distance traveled by the two cars is given as,
d = 30 t – 20 t
t = d/10 = 50/10 = 5 s.
Question
A projectile is launched at an angle to the horizontal at time t = 0. It travels over horizontal
ground, as shown.
Air resistance is negligible.
Which graph best shows the variation with t of the speed of the projectile from when it is launched
to when it lands on the ground?
Answer/Explanation
Ans:C
The speed of the projectile decreases in the beginning until it reaches the maximum height and then increases till it reaches the ground.
Since the speed is not constant, therefore option (A) is incorrect.
Since the speed is not a linear function of time and does not become zero at any point therefore options B and D are incorrect.
Question
A cannon fires a cannonball with an initial speed v at an angle ∝ to the horizontal.
Which equation is correct for the maximum height H reached?
(A) H = ( 2v)/g
(B) H = \((v^2 \sin^2 \alpha)/g\)
(C)
(D) H = \(v^2\cos^2\alpha/(2g)\)
Answer/Explanation
Ans
C
The maximum height is given by the equation,
Question
Four cars, A, B, C and D, move from rest in a straight line. The cars take the same time to
accelerate to a velocity of 60 km h–1. Their velocity–time graphs are shown.
Which car reaches a velocity of 60 km h–1 in the shortest distance?
Answer/Explanation
Ans
D