A race car traveling at +55m/s is uniformly accelerated to a velocity of +24 m/s over an 8.9-s interval. What is its displacement during this time
average velocity * time
[(55 + 24) / 2] * 8.9 = ? ... meters
suspect you mean 5.5 m/s
To find the displacement of the race car during this time interval, we can use the formula:
\(s = ut + \frac{1}{2}at^2\)
Where:
s = displacement
u = initial velocity
t = time interval
a = acceleration
Given:
u = +55 m/s (initial velocity)
v = +24 m/s (final velocity)
t = 8.9 s (time interval)
First, we need to find the acceleration (a). We can use the formula:
\(v = u + at\)
Rearranging the formula:
\(a = \frac{v - u}{t}\)
Substituting the values:
\(a = \frac{24 - 55}{8.9}\)
\(a = \frac{-31}{8.9}\)
Now, substituting the values of u, t, and a in the displacement formula:
\(s = (55)(8.9) + \frac{1}{2}\left(\frac{-31}{8.9}\right)(8.9)^2\)
\(s = 489.5 + \frac{-31}{2}(8.9)\)
\(s = 489.5 - 138.95\)
\(s = 350.55\) m
Therefore, the displacement of the race car during this time interval is 350.55 meters.
To find the displacement of the race car, we can use the formula for displacement:
Displacement = (Final velocity - Initial velocity) × Time
Given:
Initial velocity (u) = +55 m/s
Final velocity (v) = +24 m/s
Time (t) = 8.9 s
Substituting the values into the formula:
Displacement = (24 m/s - 55 m/s) × 8.9 s
To calculate the displacement, we first need to find the change in velocity, which is the difference between the final and the initial velocities:
Change in velocity = Final velocity - Initial velocity
= 24 m/s - 55 m/s
= -31 m/s
Now we can substitute the values:
Displacement = (-31 m/s) × 8.9 s
Multiply the velocity by the time:
Displacement = -275.9 m
The negative sign indicates that the displacement is in the opposite direction of the initial velocity. Therefore, the race car has a displacement of -275.9 meters during this time interval.