Kinematics: Physics 9702 (Cambridge International AS & A Level)

A cyclist rides in a straight line along a road. She travels $300\text{ m}$ due east, then turns around and rides back $120\text{ m}$ due west along the same road, coming to rest at a petrol station.

Which row gives the correct total distance travelled by the cyclist and the correct magnitude of her displacement from her starting point?

A car travels along a straight, horizontal road. Starting from rest, the car accelerates uniformly and reaches a velocity of $24\text{ m s}^{-1}$ after a time of $8.0\text{ s}$.

(a) Calculate the acceleration of the car during this $8.0\text{ s}$. [2]

(b) Calculate the distance travelled by the car during this $8.0\text{ s}$. [2]

(c) The car continues at a constant velocity of $24\text{ m s}^{-1}$ for some time. The driver then brakes, decelerating the car uniformly to rest over a distance of $60\text{ m}$. Calculate the magnitude of this deceleration. [3]

A student stands at the edge of a flat rooftop and throws a small stone vertically upwards with an initial speed of $12.0\text{ m s}^{-1}$. Air resistance is negligible. Take $g = 9.81\text{ m s}^{-2}$.

(a) Calculate the maximum height reached by the stone above the point at which it was released. [3]

(b) Calculate the total time taken for the stone to fall back to the height at which it was released. [2]

(c) The point at which the stone was released is $18.0\text{ m}$ above the ground. Calculate the speed with which the stone hits the ground. [3]

A small marble rolls off the edge of a horizontal table with a horizontal velocity of $3.50\text{ m s}^{-1}$. The table top is $0.800\text{ m}$ above the floor. Air resistance is negligible. Take $g = 9.81\text{ m s}^{-2}$.

(a) Show that the time taken for the marble to fall from the table top to the floor is $0.404\text{ s}$, to 3 significant figures. [3]

(b) Calculate the horizontal distance travelled by the marble, measured from the edge of the table to the point where it lands on the floor. [2]

(c) Calculate the vertical component of the marble's velocity just before it lands on the floor. [2]

(d) Calculate the magnitude and direction of the marble's velocity just before it lands on the floor. [3]

A delivery drone flies in a straight line. Its velocity–time graph for the flight can be described as follows: starting from rest, the drone's velocity increases uniformly to $8.0\text{ m s}^{-1}$ over the first $4.0\text{ s}$; the velocity then stays constant at $8.0\text{ m s}^{-1}$ for the next $6.0\text{ s}$; finally, the velocity decreases uniformly back to zero over a further $2.0\text{ s}$.

What is the total distance travelled by the drone during the whole $12.0\text{ s}$ flight?

A jogger runs along a straight, level path. Her displacement–time graph for a $70\text{ s}$ run can be described as follows: from $t=0$ to $t=20\text{ s}$, her displacement increases uniformly from $0$ to $100\text{ m}$; from $t=20\text{ s}$ to $t=50\text{ s}$, her displacement stays constant at $100\text{ m}$ while she stops to tie her shoelace; from $t=50\text{ s}$ to $t=70\text{ s}$, her displacement decreases uniformly from $100\text{ m}$ to $40\text{ m}$ as she jogs back part of the way.

What is the jogger's velocity during the interval $t=50\text{ s}$ to $t=70\text{ s}$?

An aircraft taxiing for takeoff starts from rest and accelerates uniformly along a straight, horizontal runway at $2.4\text{ m s}^{-2}$ for a time of $15\text{ s}$, at which point it reaches its takeoff speed.

(a) Calculate the takeoff speed of the aircraft. [2]

(b) Calculate the total distance travelled by the aircraft during this $15\text{ s}$ of acceleration. [2]

(c) Calculate the distance travelled by the aircraft during the last $5.0\text{ s}$ of this $15\text{ s}$ acceleration phase. [3]

A footballer kicks a ball from ground level on a horizontal pitch. The ball leaves her foot with an initial speed of $18.0\text{ m s}^{-1}$ at an angle of $35.0°$ above the horizontal. Air resistance is negligible. Take $g = 9.81\text{ m s}^{-2}$.

(a) Calculate the horizontal component and the vertical component of the ball's initial velocity. [2]

(b) Calculate the time taken for the ball to reach its maximum height. [2]

(c) Calculate the maximum height reached by the ball above the pitch. [2]

(d) Calculate the total time of flight before the ball lands back on the pitch. [2]

(e) Calculate the horizontal distance travelled by the ball before it first lands. [2]

A go-kart is travelling at a constant velocity of $4.0\text{ m s}^{-1}$ along a straight track when the driver presses the accelerator, giving the go-kart a uniform acceleration of $2.0\text{ m s}^{-2}$ for a time of $5.0\text{ s}$.

What is the displacement of the go-kart during this $5.0\text{ s}$?

A stone is thrown vertically downward from the top of a cliff of height $45.0\text{ m}$, with an initial speed of $6.00\text{ m s}^{-1}$. The stone falls freely under gravity and air resistance is negligible. Take $g = 9.81\text{ m s}^{-2}$.

(a) By setting up a suitable equation of motion and solving it for $t$, calculate the time taken for the stone to reach the base of the cliff. [3]

(b) Calculate the speed with which the stone hits the base of the cliff. [2]

(c) A second, identical stone is simply released from rest at the same point (i.e. dropped, not thrown) at the same instant as the first stone. Calculate the time this second stone takes to reach the base of the cliff, and hence find the difference between the two fall times. [3]