Kinematics

A car is accelerated by a constant resultant force of $300\text{ N}$ for $5.0\text{ s}$.
The variation with time of the velocity, in $\text{cm s}^{-1}$, of the car is shown.

What is the mass of the car?

Options

A   $13\text{ kg}$
B   $1000\text{ kg}$
C   $1300\text{ kg}$
D   $10\,000\text{ kg}$

An aircraft, initially stationary on a runway, takes off with a speed of $85\text{ km h}^{-1}$ in a distance of no more than $1.20\text{ km}$.
What is the minimum constant acceleration necessary for the aircraft?

Options

A   $0.23\text{ m s}^{-2}$
B   $0.46\text{ m s}^{-2}$
C   $3.0\text{ m s}^{-2}$
D   $6.0\text{ m s}^{-2}$

An object is fired upwards from horizontal ground. The object has an initial velocity of $20\text{ m s}^{-1}$ at an angle of $45^\circ$ to the horizontal. Air resistance is negligible.
Which statement describes the speed of the object after it is fired until immediately before it reaches the ground again?

Options

A   Its speed decreases to a value greater than zero, then increases to $20\text{ m s}^{-1}$.
B   Its speed decreases to a value greater than zero, then increases to a value greater than $20\text{ m s}^{-1}$.
C   Its speed decreases to zero, then increases to $20\text{ m s}^{-1}$.
D   Its speed decreases to zero, then increases to a value less than $20\text{ m s}^{-1}$.

A projectile is launched at $45^\circ$ to the horizontal with initial kinetic energy $E$.
Assuming air resistance to be negligible, what will be the kinetic energy of the projectile when it reaches its highest point?

Options

A   $0.50E$
B   $0.71E$
C   $0.87E$
D   $E$

A ball is projected vertically downwards with an initial velocity of $20\text{ m s}^{-1}$. Air resistance is negligible.

What is the displacement from its initial position of the ball after a time of $1.5\text{ s}$?

Options

A   $11\text{ m}$
B   $19\text{ m}$
C   $37\text{ m}$
D   $41\text{ m}$

Which equation of uniformly accelerated motion can be derived using only the gradient of a velocity–time graph?

Options

A   $s = \frac{1}{2}(u + v)t$
B   $s = ut + \frac{1}{2}at^2$
C   $v = u + at$
D   $v^2 = u^2 + 2as$

An object is projected horizontally from a table at time $t = 0$. The object falls in a uniform gravitational field. Air resistance is negligible.

Graphs P, Q, R and S are velocity–time graphs.

Which graphs represent the horizontal and vertical components of the velocity of the object?

Options

The graph shows the variation with time of the velocity of a car.

Which statement is correct?

Options

A   The car accelerates for $2\text{ s}$, then stops for $4\text{ s}$ and then reverses.
B   The car accelerates at $12\text{ m s}^{-2}$ for $2\text{ s}$.
C   The car travels a distance of $36\text{ m}$ in the first $4\text{ s}$.
D   The car travels a distance of $48\text{ m}$ in the last $4\text{ s}$.

A solid object of mass $1.0\text{ kg}$ falls vertically downwards in a vacuum.

When the speed of the object is $60\text{ m s}^{-1}$, an additional constant force of $50\text{ N}$ suddenly starts to act vertically upwards on the object.

What is the speed of the object $2.0\text{ s}$ after the additional force starts to act?

Options

A   $20\text{ m s}^{-1}$
B   $40\text{ m s}^{-1}$
C   $80\text{ m s}^{-1}$
D   $100\text{ m s}^{-1}$

A stone is thrown upwards and follows a curved path.

Air resistance is negligible.

Why does the path have this shape?

Options

A   The stone has a constant horizontal acceleration and constant vertical velocity.
B   The stone has a constant horizontal velocity and constant vertical acceleration.
C   The stone has a constant upward acceleration followed by a constant downward acceleration.
D   The stone has a constant upward velocity followed by a constant downward velocity.