A ball is thrown up in the air from the surface of a pond with initial velocity $20 \mathrm{m}{ \mathrm{s}}^{-1}.$ It accelerates downwards under gravity with constant acceleration $10 \mathrm{m}{ \mathrm{s}}^{-2}.$ Once it has reached its highest point it falls until it hits the surface of the pond and goes underwater. Under the water, it continues to accelerate with constant acceleration $1 \mathrm{m}{ \mathrm{s}}^{-2}$ for $1 \mathrm{s}.$ Sketch the velocity-time graphs from the given information. Take the upward direction to be positive.

A parachutist falls from a helicopter that is flying at a constant height. She accelerates downwards at a constant rate of $10 \mathrm{m}{ \mathrm{s}}^{-2}$ for $0.5 \mathrm{s}$ before the parachute opens. She then remains at constant speed for $5 \mathrm{s}.$ Sketch the velocity-time graphs from the information given. Take upwards to be the positive direction.

A firework takes off from rest and accelerates upwards for $7 \mathrm{s}$ with constant acceleration $5 \mathrm{m}{ \mathrm{s}}^{-2},$ before decelerating at a constant rate of $10 \mathrm{m}{ \mathrm{s}}^{-2}$ until it explodes at the highest point of its trajectory. Sketch the velocity-time graphs from the information given. Take upwards to be the positive direction.

The graph shows the motion of a motorcyclist when he starts travelling along a highway until reaching top speed. Find the distance covered in reaching that speed.

The graph shows the motion of a ball when it is thrown upwards in the air until it hits the ground. Find the height above the ground from which it was thrown. (Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

The sketch graph shows the motion of a boat. Find the distance the boat travels during the motion.

The graph shows the journey of a cyclist travelling in a straight line from home to school. Find the distance between her home and the school.