A car with an initial speed of 23.5 km/h accelerates at a uniform rate of 0.98 m/s2
for 4.0
s.
Find the final speed of the car.
Answer in units of m/s
23.5kmph=23500/3600=6.53m/s
v=u+ft=6.53+0.98*4=6.53+3.92=10.45m/s
To find the final speed of the car, we can use the equation for acceleration:
v = u + at,
where:
v is the final speed of the car,
u is the initial speed of the car,
a is the acceleration of the car, and
t is the time period for which the car accelerates.
Given:
u = 23.5 km/h,
a = 0.98 m/s², and
t = 4.0 s.
To solve the problem, we need to convert the initial speed from kilometers per hour (km/h) to meters per second (m/s) to be consistent with the units used for acceleration.
To convert km/h to m/s, we use the conversion factor: 1 km/h = 0.277778 m/s.
So, the initial speed in m/s is:
u = 23.5 km/h × 0.277778 m/s = 6.52776 m/s.
Now, we can substitute the given values into the equation:
v = u + at
v = 6.52776 m/s + (0.98 m/s² × 4.0 s)
v = 6.52776 m/s + 3.92 m/s
v = 10.44776 m/s.
Therefore, the final speed of the car is approximately 10.45 m/s.