Question
A car starts from rest and covers distance of 100m in one second with uniform acceleration.its acceleration is?
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Answered by
GPT-4o mini
To find the acceleration of the car, we can use the kinematic equation for uniformly accelerated motion:
\[
s = ut + \frac{1}{2} a t^2
\]
Where:
- \( s \) is the distance covered (100 m)
- \( u \) is the initial velocity (0 m/s, since the car starts from rest)
- \( a \) is the acceleration (which we need to find)
- \( t \) is the time (1 second)
Since the car starts from rest (\( u = 0 \)), the equation simplifies to:
\[
s = \frac{1}{2} a t^2
\]
Substituting the known values into the equation:
\[
100 = \frac{1}{2} a (1^2)
\]
This simplifies to:
\[
100 = \frac{1}{2} a
\]
To isolate \( a \), multiply both sides by 2:
\[
200 = a
\]
Thus, the acceleration of the car is:
\[
a = 200 \, \text{m/s}^2
\]
\[
s = ut + \frac{1}{2} a t^2
\]
Where:
- \( s \) is the distance covered (100 m)
- \( u \) is the initial velocity (0 m/s, since the car starts from rest)
- \( a \) is the acceleration (which we need to find)
- \( t \) is the time (1 second)
Since the car starts from rest (\( u = 0 \)), the equation simplifies to:
\[
s = \frac{1}{2} a t^2
\]
Substituting the known values into the equation:
\[
100 = \frac{1}{2} a (1^2)
\]
This simplifies to:
\[
100 = \frac{1}{2} a
\]
To isolate \( a \), multiply both sides by 2:
\[
200 = a
\]
Thus, the acceleration of the car is:
\[
a = 200 \, \text{m/s}^2
\]
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