Give example of a motion where $x > 0$, $v < 0$, $a > 0$ at a particular instant.
Let the motion is represented by
$x(t)=4+5 \mathrm{e}^{-\gamma t}$
Let $A>B$ and $\gamma>0$
Now velocity $x(t)=\frac{d x}{d t}=-5(7) e^{-7 t}$
Acceleration $a(t)=\frac{d x}{d t}=5(7)^{2} e^{-7 t}$
Suppose we are considering any instant $t$, then from Eq. (i), we can say that $x(t)>0 ; v(t)<0$ and $a>0$
$x(t)=4+5 \mathrm{e}^{-\gamma t}$
Let $A>B$ and $\gamma>0$
Now velocity $x(t)=\frac{d x}{d t}=-5(7) e^{-7 t}$
Acceleration $a(t)=\frac{d x}{d t}=5(7)^{2} e^{-7 t}$
Suppose we are considering any instant $t$, then from Eq. (i), we can say that $x(t)>0 ; v(t)<0$ and $a>0$
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- [JEE MAIN 2021]
For the velocity-time graph shown in the figure, in a time interval from $t=0$ to $t=6\,s$, match the following columns.
Colum $I$
Colum $II$
$(A)$ Change in velocity
$(p)$ $-5 / 3\,Sl$ unit
$(B)$ Average acceleration
$(q)$ $-20\,SI$ unit
$(C)$ Total displacement
$(r)$ $-10\,SI$ unit
$(D)$ Acceleration at $t=3\,s$
$(s)$ $-5\,SI$ unit
For the velocity-time graph shown in the figure, in a time interval from $t=0$ to $t=6\,s$, match the following columns.
| Colum $I$ | Colum $II$ |
| $(A)$ Change in velocity | $(p)$ $-5 / 3\,Sl$ unit |
| $(B)$ Average acceleration | $(q)$ $-20\,SI$ unit |
| $(C)$ Total displacement | $(r)$ $-10\,SI$ unit |
| $(D)$ Acceleration at $t=3\,s$ | $(s)$ $-5\,SI$ unit |
For the acceleration-time $(a-t)$ graph shown in figure, the change in velocity of particle from $t=0$ to $t=6 \,s$ is ........ $m / s$
For the acceleration-time $(a-t)$ graph shown in figure, the change in velocity of particle from $t=0$ to $t=6 \,s$ is ........ $m / s$
Acceleration-time graph is given. If initial velocity is $5\,\,m/s,$ then velocity after $2$ $seconds$ is.......$m/s$
Acceleration-time graph is given. If initial velocity is $5\,\,m/s,$ then velocity after $2$ $seconds$ is.......$m/s$