A particle moves along a straight line so that the distance covered in $t$ seconds is $s(t)=4t^2-3t+5$ metres. Find (a) the average velocity between $t=1$ and $t=3$, and (b) the instantaneous velocity at $t=2$.

**(a) Average velocity.** $s(3)=4(9)-3(3)+5=36-9+5=32$ and $s(1)=4(1)-3(1)+5=4-3+5=6$. So $$\text{average velocity} = \frac{s(3)-s(1)}{3-1} = \frac{32-6}{2} = \frac{26}{2} = 13\text{ m/s}.$$ …

A particle moves along a straight line so that the

Miscellaneous · Q34

t

(a) the average velocity between

t=1

and

t=3

, and

(b) the instantaneous velocity at

t=2

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Concept understanding — Derivative as Rate of Change

For a quantity that changes with time -- most

concretely, the distance $s(t)$ covered by a moving particle -- the average rate of change over

an interval $[t,t+\Delta t]$ is $\Delta s/\Delta t$ , the change in the quantity divided by the …

←Previous questionQ33 — Find the derivative of y=xsin x+cos x.→Next questionExample 1 — If limx→ af(x)=5 and limx→ ag(x)=-2, find the value of limx→ abig[3f(x…

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Miscellaneous · Q34

t

(a) the average velocity between

t=1

and

t=3

, and

(b) the instantaneous velocity at

t=2

West Bengal WbchseNCERTSubjectiveImportance★★★★★est

9% · 3/34 Questions

You're viewing a preview — the full solution, concept, methods & PYQ mapping are locked.

Concept understanding — Derivative as Rate of Change

For a quantity that changes with time -- most

concretely, the distance $s(t)$ covered by a moving particle -- the average rate of change over

an interval $[t,t+\Delta t]$ is $\Delta s/\Delta t$ , the change in the quantity divided by the …

←Previous questionQ33 — Find the derivative of y=xsin x+cos x.→Next questionExample 1 — If limx→ af(x)=5 and limx→ ag(x)=-2, find the value of limx→ abig[3f(x…

Q.A particle moves along a straight line so that the distance covered in $t$ seconds is $s(t)=4t^2-3t+5$ metres. Find

Concept understanding — Derivative as Rate of Change

Q.A particle moves along a straight line so that the distance covered in $t$ seconds is $s(t)=4t^2-3t+5$ metres. Find

Concept understanding — Derivative as Rate of Change

Q.A particle moves along a straight line so that the distance covered in ttt seconds is s(t)=4t2−3t+5s(t)=4t^2-3t+5s(t)=4t2−3t+5 metres. Find

Concept understanding — Derivative as Rate of Change

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Q.A particle moves along a straight line so that the distance covered in ttt seconds is s(t)=4t2−3t+5s(t)=4t^2-3t+5s(t)=4t2−3t+5 metres. Find

Concept understanding — Derivative as Rate of Change

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Q.A particle moves along a straight line so that the distance covered in $t$ seconds is $s(t)=4t^2-3t+5$ metres. Find

Unlock the full solution

Q.A particle moves along a straight line so that the distance covered in $t$ seconds is $s(t)=4t^2-3t+5$ metres. Find

Unlock the full solution