New chat PYQ Library Doubts Rank report

Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →

Motion in A Straight Line question

2022 · 29 Jul · Shift 1 · Q50

Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.

PYQ Library
JEE Main
Physics
Motion in A Straight Line
2022 · 29 Jul · Shift 1 · Q50

Motion in A Straight Line question

2022 · 29 Jul · Shift 1 · Q50

JEE MainPhysicsMotion in A Straight LineMCQ+4 / −1

If

\mathrm{t}=\sqrt{x}+4

, then

\left(\frac{\mathrm{d} x}{\mathrm{~d} t}\right)_{\mathrm{t}=4}

is :

A
4
B
zero
C
8
D
16

View written solutionFree

Correct answer: B

Given relation

$t = \sqrt{x} + 4$

We need to find

$\left(\frac{dx}{dt}\right)_{t=4}$
Express $x$ in terms of $t$

From

$t - 4 = \sqrt{x}$

squaring both sides,

$x = (t-4)^2$
Differentiate with respect to $t$

$\frac{dx}{dt} = 2(t-4)$
Evaluate at $t=4$

$\left(\frac{dx}{dt}\right)_{t=4} = 2(4-4) = 0$
Check options
- A: $4$ ❌
- B: $0$ ✅
- C: $8$ ❌
- D: $16$ ❌

Therefore, the correct answer is B: zero.

More from Motion in A Straight Line

A juggler throws balls vertically upwards with same initial velocity in air. When the first ball reaches its highest position, he throws the next ball. Assuming the juggler throws n balls per second, the maximum height the balls can reach…2022 · MCQ
A ball is released from a height h. If $t_{1}$ and $t_{2}$ be the time required to complete first half and second half of the distance respectively. Then, choose the correct relation between $t_{1}$ and $t_{2}$ .2022 · MCQ
Two balls A and B are placed at the top of 180 m tall tower. Ball A is released from the top at t = 0 s. Ball B is thrown vertically down with an initial velocity 'u' at t = 2 s. After a certain time, both balls meet 100 m above the…2022 · MCQ
A small toy starts moving from the position of rest under a constant acceleration. If it travels a distance of 10m in t s, the distance travelled by the toy in the next t s will be :2022 · MCQ
The velocity-displacement graph describing the motion of bicycle is shown in the figure. The acceleration-displacement graph of the bicycle's motion is best described by : Includes diagram2021 · MCQ
A car accelerates from rest at a constant rate $α$ for some time after which it decelerates at a constant rate $β$ to come to rest. If the total time elapsed is t seconds, the total distance travelled is :2021 · MCQ
The velocity of a particle is v = v0 + gt + Ft2. Its position is x = 0 at t = 0; then its displacement after time (t = 1) is :2021 · MCQ
A rubber ball is released from a height of 5 m above the floor. It bounces back repeatedly, always rising to $\frac{81}{100}$ of the height through which it falls. Find the average speed of the ball. (Take g = 10 ms $-$ 2)2021 · MCQ