First slide

The 3 equation for uniform acc

Question

Two cars start in a race with velocities $u_{1}$ and $u_{2}$ and travel in a straight line with acceleration ‘ $α$ ’ and $β$ . If both reach the finish line at the same time, the range of the race is

Moderate

A

$\frac{2 (u_{1} - u_{2})}{{(β - α)}^{2}} (u_{1} β - u_{2} α)$
B

$\frac{2 (u_{1} - u_{2})}{β + α} (u_{1} α - u_{2} β)$
C

$\frac{2 {(u_{1} - u_{2})}^{2}}{{(β - α)}^{2}}$
D
$\frac{2 u_{1} u_{2}}{α β}$

Solution

$s = u_{1} t + \frac{1}{2} α t^{2} (f o r f i r s t c a r) s = u_{2} t + \frac{1}{2} β t^{2} (f o r s e c o n d c a r) 0 = (u_{1} - u_{2}) t + \frac{1}{2} (α - β) t^{2} t = \frac{2 (u_{2} - u_{1})}{(β - α)} s = \frac{2 (u_{2} - u_{1}) u_{1}}{β - α} + \frac{1}{2} α {[\frac{(u_{2} - u_{1})}{(β - α)}]}^{2} S i m p l i f y i n g, s = \frac{2 (u_{1} - u_{2}) (u_{1} β - u_{2} α)}{{(β - α)}^{2}}$

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