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

To find the force vector F, we use Newton's second law, where F = ma. We first determine the change in velocity:

$\Delta v = (7i + 10j) - (2i - 5j) = (5i + 15j)$.

Now, since this change occurs over the time interval t = 5 s, we calculate the acceleration:

$a = \frac{\Delta v}{\Delta t} = \frac{(5i + 15j)}{5} = i + 3j$.

Given the mass m = 2 kg, we can now find the force:

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

For P to be moving parallel to the i direction, its velocity in the j direction must be zero. Thus, we set:

$v = u + at$ $= (2i - 5j) + (i + 3j) t$

Setting the j-component to zero:

$-5 + 3t = 0 \implies t = \frac{5}{3}$.

Therefore, the value of t when P is moving parallel to i is ( t = \frac{5}{3} ) seconds.