What does the slope of a distance-time graph represent, and what does the area under a velocity-time graph represent?

A stone is dropped from a height of 45 m. Find the time it takes to reach the ground and its speed on landing. Take g = 10 m s⁻².

A body travels with a uniform velocity of 15 m s⁻¹ for 4 s and then accelerates at 2 m s⁻² for a further 3 s. Find the total distance travelled.

A train starting from rest attains a speed of 72 km h⁻¹ in 1 minute. Find its acceleration and the distance covered.

A body starts from rest and moves with a uniform acceleration of 2 m s⁻² for 5 s. Find its final velocity and the distance travelled.

A car moving at 20 m s⁻¹ is brought to rest in 5 s. Find its retardation and the distance it travels in that time.

Sketch and describe the velocity-time graph of a body moving with uniform acceleration from rest.