A particle P of mass 2 kg is moving under the action of a constant force F newtons - Edexcel - A-Level Maths Mechanics - Question 4 - 2011 - Paper 1

We need to find the force vector F. The change in velocity over the time interval is:

$v(t=5) - v(t=0) = (7i + 10j) - (2i - 5j) = (7 - 2)i + (10 + 5)j = 5i + 15j$

The time interval is (5 s). Using the formula for acceleration (a = (v_f - v_i) / t):

$a = \frac{(5i + 15j)}{5} = i + 3j$

Now, using Newton's second law (F = ma), where the mass m = 2 kg:

$F = 2(i + 3j) = 2i + 6j$

For the particle P to be moving parallel to the i direction, the j-component of its velocity must be zero. Thus, we require:

$v = u + at$

Where:

• (u = (2i - 5j))
• (a = (i + 3j))

Setting the j-component to zero:

$(-5 + 3t) = 0 \\Rightarrow 3t = 5 \\Rightarrow t = \frac{5}{3}$

Thus, the time at which P is moving parallel to i is (t = \frac{5}{3} s.