A particle is moving in one dimension (along | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given position function: $x = -3t^3 + 18t^2 + 16t$.Velocity $v$ is the first derivative of position with respect to time: $v = \frac{dx}{dt} = \fr

Vedclass · Accepted Answer

$52$

Vedclass · Answer

(B) Given position function: $x = -3t^3 + 18t^2 + 16t$.Velocity $v$ is the first derivative of position with respect to time: $v = \frac{dx}{dt} = \frac{d}{dt}(-3t^3 + 18t^2 + 16t) = -9t^2 + 36t + 16$.Acceleration $a$ is the derivative of velocity with respect to time: $a = \frac{dv}{dt} = \frac{d}{dt}(-9t^2 + 36t + 16) = -18t + 36$.Set acceleration to zero to find the time: $-18t + 36 = 0 \implies 18t = 36 \implies t = 2 \,s$.Substitute $t = 2 \,s$ into the velocity equation: $v = -9(2)^2 + 36(2) + 16$.$v = -9(4) + 72 + 16 = -36 + 72 + 16 = 52 \,m/s$.

$t (s)$	$0$	$1$	$2$	$3$
$x (m)$	$-2$	$0$	$6$	$16$

Similar Questions

The position of a particle moving along the $X-$axis at certain times is given below. Which of the following describes the motion correctly?
$t (s)$ $0$ $1$ $2$ $3$
$x (m)$ $-2$ $0$ $6$ $16$

Explain the acceleration.

The acceleration $(a)$-time $(t)$ graph for a particle moving along a straight line starting from rest is shown in the figure. Which of the following graphs is the best representation of the variation of its velocity $(v)$ with time $(t)$?

$A$ body is moving with variable acceleration $a$ along a straight line. The average acceleration of the body in the time interval $t_1$ to $t_2$ is

What will be the change in the speed of a moving object if both speed and acceleration are positive or both are negative?

Vedclass Test Series

Exam Paper Generator

Online Exam Module