Year 2 Mechanics Revision

Answer explanation

v(t) = ds/dt = 3t² - 6t

v(5) = 3×5² - 6×5

= 45 m/s

If a = (4t + 5)i + 6tj m/s² and the particle is initially at rest, its velocity when t = 4 is

• 15i - 3j

• 26i + 24j

• 52i + 48j

• 15i + 25j

Find the total moment of this system of forces, in Nm, about the point O.

Answer explanation

Total moment, remmbering that clockwise moments are negative is

3×5 - 7×8

= -41 Nm

A uniform beam AB of mass 10 kg is freely hinged at A and is kept horizontal by a string from B to a pivot vertically above A. The string makes an angle of 30° with the beam.

Find the tension, in newtons, in the string.

Take g as 9.8 m/s²

Answer explanation

A light rod, 8 metres long, has masses of 1kg, 3kg and 2kg placed 2m, 4m and 8m respectively from one end, O.

What is the distance of the centre of mass from O, in metres?

Answer explanation

A heavy rod AB mass 25kg and length 2.4m is hinged at A to a point on a vertical wall. It is kept horizontal by a chain attached to B and a point 1.5m vertically above A. The bar carries an additional mass of 10kg, 1.8m from A.

Find the tension, in newtons in the chain, correct to 3 s.f.

Answer explanation

The displacement $s$ metres of a particle after $t$  seconds is given by

 $s=t^4-4t$ 

What is the time, in seconds, at which the particle is stationary?

The acceleration $a$ m/s² after $t$ seconds of a particle, initially at rest, is given by
 $a=t^3-2t$ 
What is the velocity in m/s after 2 seconds?

The velocity of a particle is modelled by

v = (3t²i + 10tj) m/s.

Given that r = (4i - 4j)m when t = 0.

Find the distance of the particle, in metres, from the origin when t = 2.

A sledge of mass 30 kg starts from rest and is pulled with a force of 50 N against a resistance of 25 N for a distance of 15 m.

How fast is it then going in m/s?