Question

two forces are applied to a 0.45kg toy car, f1 = (2.5n, 1.5n) and a second force f2 = (-2.25n, -0.75n). if the car starts from rest, calculate the modulus of its velocity after 5 seconds.

Answer 1

Let us determine the total force applied to the car. We may consider the projections of forces onto two axes:

$F_x = F_{1,x} + F_{2,x} = 2.5\,\mathrm{N} + (-2.25\,\mathrm{N}) = 0.25\,\mathrm{N}, \\ F_y = F_{1,y} + F_{2,y} = 1.5\,\mathrm{N} + (-0.75\,\mathrm{N}) = 0.75\,\mathrm{N}.$

The total force is $F = \sqrt{F_x^2+F_y^2} \approx 0.79\,\mathrm{N}.$

The acceleration is $a = \dfrac{F}{m} = \dfrac{0.79\,\mathrm{N}}{0.45\,\mathrm{kg}} = 1.76\,\mathrm{m/s^2}.$

The velocity after 5 seconds $v = at = 8.8\,\mathrm{m/s}.$