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Q10. A car has an initial velocity of
300m// minute. It travels a distance of
0.5km in 20 seconds. Use the appropriate formula to calculate the acceleration of the car in
m//s^(2).

v=u+at quad s=ut+(1)/(2)at^(2)quadv^(2)=u^(2)+2as
where
a= constant acceleration,
u= initial velocity,
v= final velocity,
s= displacement fror the position when
t=0 and
t= time taken.

Q $10$ . A car has an initial velocity of $300 \mathrm{~m} /$ minute. It travels a distance of $0.5 \mathrm{~km}$ in $20$ seconds. Use the appropriate formula to calculate the acceleration of the car in $\mathrm{m} / \mathrm{s}^{2}$ . $\newline$ $v=u+a t \quad s=u t+\frac{1}{2} a t^{2} \quad v^{2}=u^{2}+2 a s$ $\newline$ where $a=$ constant acceleration, $u=$ initial velocity, $v=$ final velocity, $s=$ displacement fror the position when $t=0$ and $t=$ time taken.

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Relate position, velocity, speed, and acceleration using derivatives

Full solution

Q. Q

10

. A car has an initial velocity of

300 \mathrm{~m} /

minute. It travels a distance of

0.5 \mathrm{~km}

in

20

seconds. Use the appropriate formula to calculate the acceleration of the car in

\mathrm{m} / \mathrm{s}^{2}

.

\newline

v=u+a t \quad s=u t+\frac{1}{2} a t^{2} \quad v^{2}=u^{2}+2 a s

\newline

where

a=

constant acceleration,

u=

initial velocity,

v=

final velocity,

s=

displacement fror the position when

t=0

and

t=

time taken.

Convert Distance to Meters: First, convert the distance from kilometers to meters. $0.5$ km is $500$ meters.
Convert Time to Minutes: Next, convert the time from seconds to minutes. $20$ seconds is $\frac{1}{3}$ of a minute.
Calculate Final Velocity: Now, calculate the final velocity using the formula $s = ut + \frac{1}{2}at^2$ . We have $s (500\,\text{m})$ , $u (300\,\text{m}/\text{minute})$ , and $t (\frac{1}{3}\,\text{minute})$ . But we need to convert $u$ to $\text{m}/\text{s}$ before we can use the formula.
Convert Initial Velocity: Convert the initial velocity from m/minute to m/s. There are $60$ seconds in a minute, so $300 \, \text{m}/\text{minute}$ is $5 \, \text{m}/\text{s}.$
Use Formula to Find 'a': Now we can use the formula $s = ut + \frac{1}{2}at^2$ to find 'a'. Plugging in the numbers, we get $500 = (5)(\frac{1}{3}) + \frac{1}{2}a(\frac{1}{3})^2$ .
Simplify Equation: Simplify the equation: $500 = \frac{5}{3} + \left(\frac{1}{2}\right)a\left(\frac{1}{9}\right).$
Multiply by $9$ : Multiply both sides by $9$ to get rid of the fraction: $4500 = 15 + (\frac{1}{2})a$ .
Subtract $15$ : Subtract $15$ from both sides: $4485 = \left(\frac{1}{2}\right)a$ .
Solve for 'a': Multiply both sides by $2$ to solve for 'a': $a = 8970$ .

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