Motion and Rates

A stone is thrown upwards and then falls back onto the ground.

Which of the following is true at the top of its flight?

• Neither the velocity nor the acceleration is zero.

• Both the velocity and the acceleration is zero.

• The acceleration is zero, but the velocity is not zero.

• The velocity is zero, but the acceleration is not zero.

A truck took one hour to travel south 60 km, then took two hours to travel north 100 km, then took another two hours to travel south 120 km.

What was the average speed at which the truck was travelling over these five hours?

• The average speed cannot be determined from this data.

• The velocity is positive and the acceleration is positive.

• The velocity is negative and the acceleration is positive.

• The velocity is positive and the acceleration is negative.

• The velocity is negative and the acceleration is negative.

The acceleration of a particle is given by 𝑥̈ = 40 cos 2𝑡, in units of metres and seconds. At time zero, the displacement and the velocity are both zero. At which of the following times is the particle 5 metres on the positive side of the origin?

• 6030

• 6931

• 485

• 452

• 1140 litres

• 1740 litres

• 163 litres

• 1673 litres

The sides of a square have length 𝑥 metres and are increasing at a rate of 0.2 m/s. When the side of the square is 4 metres long, at what rate is the area of the square increasing?

• 0.8 m²/s

• 1.2 m²/s

• 1.6 m²/s

• 2.4 m²/s