If a car starts from rest and accelerates at 6.0 m/sec2 for 6.0 seconds. how far did it travel and how fast was it moving at the end of the 6.0 seconds
Assemble the data first:
Initial velocity = vi = 0m/s
Acceleration = a = 6m/s2
Time = t = 6s
Distance = S = ??
Final velocity = vf = ??
Now using equations of motion:
FOR DISTANCE:
Since,
S = vit + 1/2at2
Put in the values,
S = 0*6 + 1/2*6*(6)2
S = 0 + 1/2*6*36
S - 108m
FOR FINAL VELOCITY
Both remaining equations of motion can be used.
Method # 01:
Using equation;
2aS = vf2 - vi2
2*6*108 = vf2-0
1296 = vf2
vf2 = 1296
vf = square root of 1296
vf = 36m/s
OR
Methos # 02:
Using equation;
vf = vi + at
vf = 0 + 6*6
vf = 36m/s.
Hope it helps.
To find the distance traveled by the car, you can use the formula:
distance = initial velocity * time + 0.5 * acceleration * time^2
In this case, the car starts from rest, so the initial velocity is 0 m/s. The acceleration is given as 6.0 m/s^2, and the time is 6.0 seconds. Plugging these values into the formula, we get:
distance = 0 * 6.0 + 0.5 * 6.0 * 6.0 = 0 + 0.5 * 36 = 18 meters
Therefore, the car traveled a distance of 18 meters.
To find the final velocity of the car after 6.0 seconds, you can use the formula:
final velocity = initial velocity + acceleration * time
Again, the initial velocity is 0 m/s, the acceleration is 6.0 m/s^2, and the time is 6.0 seconds. Plugging these values into the formula, we get:
final velocity = 0 + 6.0 * 6.0 = 0 + 36 = 36 m/s
Therefore, the car was moving at a speed of 36 m/s at the end of the 6.0 seconds.