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June 2018 p42 q4
3358
A particle P moves in a straight line ABCD with constant acceleration. The distances AB and BC are 100 m and 148 m respectively. The particle takes 4 s to travel from A to B and also takes 4 s to travel from B to C.
Show that the acceleration of P is 3 m s-2 and find the speed of P at A.
P reaches D with a speed of 61 m s-1. Find the distance CD.
Solution
(i) Using the equation of motion:
\(s = ut + \frac{1}{2}at^2\)
For AB:
\(100 = 4u + 8a\)
For BC:
\(148 = 4v + 8a\)
Using the equation \(v = u + at\) for AB to BC:
\(v = u + 4a\)
Substitute \(v = u + 4a\) into the equation for BC: