A car is traveling due west at 20m/s.find the velocity of the car after 3s if it’s acceleration is 1m/s2 due East . Assume that the acceleration remains constant.
what does acceleration mean?
Every second, the velocity increases by 1 m/s
So, after 3 seconds, it has increased by 3 m/s
But, the acceleration is in the opposite direction, so v decreases by 3 m/s
To find the velocity of the car after 3 seconds, we can use the formula:
v = u + at
where:
v = final velocity
u = initial velocity
a = acceleration
t = time
In this case, the car is traveling due west at 20 m/s, so the initial velocity (u) is -20 m/s (negative because it is in the opposite direction). The acceleration (a) is 1 m/s^2 due east. The time (t) is 3 seconds.
Plugging these values into the formula, we have:
v = -20 m/s + (1 m/s^2)(3 s)
v = -20 m/s + 3 m/s
v = -17 m/s
Therefore, the velocity of the car after 3 seconds is -17 m/s, indicating that it is still traveling in the west direction but at a slower speed.
To find the velocity of the car after 3 seconds, we can use the formula: final velocity = initial velocity + (acceleration × time)
Given:
Initial velocity (u) = 20 m/s (due west)
Acceleration (a) = 1 m/s² (due east)
Time (t) = 3 seconds
1. Convert the initial velocity to meters per second (m/s):
Since the initial velocity is already in meters per second, no conversion is needed.
2. Identify the direction of the acceleration:
The acceleration is given as 1 m/s² due east. Since it is in the opposite direction of the initial velocity (which is due west), we need to consider the acceleration as negative.
3. Calculate the final velocity using the formula:
final velocity (v) = u + (a × t)
Substituting the given values:
v = 20 m/s + (-1 m/s² × 3 s)
v = 20 m/s - 3 m/s
v = 17 m/s
Therefore, the velocity of the car after 3 seconds will be 17 m/s in the westward direction.