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Standard VIII

Physics

Acceleration

If a body is ...

Question

If a body is moving with a uniform acceleration $a_{1}$ for time $t_{1}$ and with uniform acceleration $a_{2}$ for time $t_{2}$ , then its average acceleration is:

\frac{a_{1} + a_{2}}{t_{1} t_{2}}

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\frac{a_{1} + a_{2}}{t_{1} + t_{2}}

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\frac{a_{1} t_{2} + a_{2} t_{2}}{t_{1} + t_{2}}

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\frac{a_{1} t_{1} + a_{2} t_{2}}{a_{1} a_{2}}

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Solution

The correct option is C $\frac{a_{1} t_{2} + a_{2} t_{2}}{t_{1} + t_{2}}$
Velocity increment in time $t_{1}$ will be $a_{1} t_{1}$ and
velocity increment in time $t_{2}$ will be $a_{2} t_{2}$
So net increment in velocity in time $t_{1} + t_{2}$ will be $a_{1} t_{1} + a_{2} t_{2}$

So average acceleration will be $\frac{net change in velocity}{Toatl time} = \frac{a_{1} t_{1} + a_{2} t_{2}}{t_{1} + t_{2}}$
Option C is correct.

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If a body is moving with a uniform acceleration a1 for time t1 and with uniform acceleration a2 for time t2, then its average acceleration is:

The correct option is C a1t2+a2t2t1+t2Velocity increment in time t1 will be a1t1 and velocity increment in time t2 will be a2t2So net increment in velocity in time t1+t2 will be a1t1+a2t2So average acceleration will be net change in velocityToatl time=a1t1+a2t2t1+t2Option C is correct.

If a body is moving with a uniform acceleration $a_{1}$ for time $t_{1}$ and with uniform acceleration $a_{2}$ for time $t_{2}$ , then its average acceleration is: