(B) The displacement of the particle is given by the equation $s = 2t^2 + 2t + 4$.To find the velocity $v$,we differentiate the displacement $s$ with

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(B) The displacement of the particle is given by the equation $s = 2t^2 + 2t + 4$.To find the velocity $v$,we differentiate the displacement $s$ with respect to time $t$:$v = \frac{ds}{dt} = \frac{d}{dt}(2t^2 + 2t + 4) = 4t + 2$.To find the acceleration $a$,we differentiate the velocity $v$ with respect to time $t$:$a = \frac{dv}{dt} = \frac{d}{dt}(4t + 2) = 4$.Thus,the acceleration of the particle is $4 \ m/s^2$.

Class 11 Physics Motion in Straight Line Acceleration and its graph

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The displacement of a particle,moving in a straight line,is given by $s = 2t^2 + 2t + 4$,where $s$ is in metres and $t$ is in seconds. The acceleration of the particle is ........ $m/s^2$.

A
$2$
B
$4$
C
$6$
D
$8$

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Motion in Straight Line

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Acceleration and its graph

The displacement is given by $x = 2t^2 + t + 5$,the acceleration at $t = 2 \ s$ is ......... $m/s^2$.

Easy

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Let $\vec v$ and $\vec a$ denote the velocity and acceleration respectively of a body in one-dimensional motion. Which of the following statements is correct regarding the speed of the body?

Medium

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Suggest a suitable physical situation for the following $a-t$ graph.

Easy

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The acceleration-time graph for a particle moving along the $x$-axis is shown in the figure. If the initial velocity of the particle is $-5 \, m/s$, the velocity at $t = 8 \, s$ is ....... $m/s$.

Medium

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$A$ body in one-dimensional motion has zero speed at an instant. At that instant,it must have:

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The displacement of a particle,moving in a straight line,is given by $s = 2t^2 + 2t + 4$,where $s$ is in metres and $t$ is in seconds. The acceleration of the particle is ........ $m/s^2$.

Similar Questions

The displacement is given by $x = 2t^2 + t + 5$,the acceleration at $t = 2 \ s$ is ......... $m/s^2$.

Let $\vec v$ and $\vec a$ denote the velocity and acceleration respectively of a body in one-dimensional motion. Which of the following statements is correct regarding the speed of the body?

Suggest a suitable physical situation for the following $a-t$ graph.

The acceleration-time graph for a particle moving along the $x$-axis is shown in the figure. If the initial velocity of the particle is $-5 \, m/s$, the velocity at $t = 8 \, s$ is ....... $m/s$.

$A$ body in one-dimensional motion has zero speed at an instant. At that instant,it must have:

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