First slide

The 3 equation for uniform acc

Question

A particle is moving with uniform acceleration along a straight line ABC. Its velocity of at A and C are 5 m/s 25 m/s respectively. If BC - 2 AB, find the ratio of time of travel from A to B to that from B to C

Moderate

A

1:1
B

5:2
C

2:1
D

1:4

Solution

See figure
$v^{2} = u^{2} + 2 as or v^{2} - 25 = 2 as . . . . (1)$
and $(25)^{2} = v^{2} + 4 as$
or 625 - v² = 4 as ..(2)
Dividing eq. (1) by eq. (2), we get
$\frac{v^{2} - 25}{625 - v^{2}} = \frac{1}{2} or 2 v^{2} - 50 = 625 - v^{2}$
or 3 v² =675 or v² = 225 or V = 15 m/s
For uniform acceleration, [(v - u) / t]should be constant.
$\begin{array}{l} ∴ \frac{15 - 5}{t_{1}} = \frac{25 - 15}{t_{2}} or \frac{10}{t_{1}} = \frac{10}{t_{2}} \\ or \frac{t_{1}}{t_{2}} = \frac{1}{1} \end{array}$

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