A car accelerates from rest at a constant rate $\alpha $ for some time, after which it decelerates at a constant rate $\beta $ and comes to rest. If the total time elapsed is $t$, then the maximum velocity acquired by the car is
A car accelerates from rest at a constant rate $\alpha $ for some time, after which it decelerates at a constant rate $\beta $ and comes to rest. If the total time elapsed is $t$, then the maximum velocity acquired by the car is
- [IIT 1978]
- [AIPMT 1994]
- A
$\left( {\frac{{{\alpha ^2} + {\beta ^2}}}{{\alpha \beta }}} \right)\,t$
- B
$\left( {\frac{{{\alpha ^2} - {\beta ^2}}}{{\alpha \beta }}} \right)\,t$
- C
$\frac{{(\alpha + \beta )\,t}}{{\alpha \beta }}$
- D
$\frac{{\alpha \beta \,t}}{{\alpha + \beta }}$
Similar Questions
A particle starts from rest. Its acceleration $(a)$ versus time $(t)$ is as shown in the figure. The maximum speed of the particle will be.....$m/s$
- [IIT 2004]
A body is at rest at $x=0$. At $t=0$, it starts moving in the positive $x-$ direction with a constant acceleration. At the same instant another body passes through $x=0$ moving in the positive $x$ direction with a constant speed. The position of the first body is given by $x_{1} (t)$ after time $t$ and that of the second body by $x_{2}(t)$ after the same time interval. Which of the following graphs correctly describe $\left(x_{1}-x_{2}\right)$ as a function of time $t$?
A body is at rest at $x=0$. At $t=0$, it starts moving in the positive $x-$ direction with a constant acceleration. At the same instant another body passes through $x=0$ moving in the positive $x$ direction with a constant speed. The position of the first body is given by $x_{1} (t)$ after time $t$ and that of the second body by $x_{2}(t)$ after the same time interval. Which of the following graphs correctly describe $\left(x_{1}-x_{2}\right)$ as a function of time $t$?
- [AIEEE 2008]
The initial velocity of a particle moving along $x$-axis is $u$ (at $t=0$ and $x=0$ ) and its acceleration $a$ is given by $a=k x$. Which of the following equation is correct between its velocity $(v)$ and position $(x)$ ?
The initial velocity of a particle moving along $x$-axis is $u$ (at $t=0$ and $x=0$ ) and its acceleration $a$ is given by $a=k x$. Which of the following equation is correct between its velocity $(v)$ and position $(x)$ ?
From the $v-t$ graph, the
From the $v-t$ graph, the
Acceleration versus time graph of a body starting from rest is shown in the figure. The velocity versus time graph of the body is given by
Acceleration versus time graph of a body starting from rest is shown in the figure. The velocity versus time graph of the body is given by