The acceleration of a particle is increasing linearly with time $t$ as $bt$. The particle starts from the origin with an initial velocity ${v_0}$. The distance travelled by the particle in time $t$ will be
The acceleration of a particle is increasing linearly with time $t$ as $bt$. The particle starts from the origin with an initial velocity ${v_0}$. The distance travelled by the particle in time $t$ will be
${v_0}t + \frac{1}{3}b{t^2}$
${v_0}t + \frac{1}{3}b{t^3}$
${v_0}t + \frac{1}{6}b{t^3}$
${v_0}t + \frac{1}{2}b{t^2}$
The acceleration of a particle is increasing linearly with time $t$ as $bt$. The particle starts from the origin with an initial velocity ${v_0}$. The distance travelled by the particle in time $t$ will be
$\frac{{dv}}{{dt}} = bt \Rightarrow dv = bt\;dt \Rightarrow v = \frac{{b{t^2}}}{2} + {K_1}$
At $t = 0,\;v = {v_0} \Rightarrow {K_1} = {v_0}$
We get $v = \frac{1}{2}b{t^2} + {v_0}$
Again $\frac{{dx}}{{dt}} = \frac{1}{2}b{t^2} + {v_0} \Rightarrow x = \frac{1}{2}\frac{{b{t^3}}}{3} + {v_0}t + {K_2}$
At $t = 0,\;x = 0 \Rightarrow {K_2} = 0$
$\therefore x = \frac{1}{6}b{t^3} + {v_0}t$
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