Given the scenario: a sports car of mass 1000 kilograms accelerates uniformly from rest to a speed of 30 meters per second. To analyze this, we can use the kinematic equations for uniform acceleration. Since the car starts from rest, the initial velocity u=0u=0u=0 m/s, and the final velocity v=30v=30v=30 m/s. If the time ttt taken to reach this speed is known, acceleration aaa can be calculated using:
v=u+at ⟹ a=v−utv=u+at\implies a=\frac{v-u}{t}v=u+at⟹a=tv−u
If the time is not given, but the distance sss traveled during acceleration is known, acceleration can be found using:
v2=u2+2as ⟹ a=v2−u22sv^2=u^2+2as\implies a=\frac{v^2-u^2}{2s}v2=u2+2as⟹a=2sv2−u2
Similarly, the distance traveled during acceleration can be found by:
s=ut+12at2s=ut+\frac{1}{2}at^2s=ut+21at2
or
s=(u+v)2ts=\frac{(u+v)}{2}ts=2(u+v)t
For example, if a 500-kilogram sports car accelerates uniformly from rest to 30 m/s in 6 seconds, the distance traveled during this time is approximately 90 meters
. Hence, for a 1000-kilogram sports car accelerating uniformly from rest to 30 m/s, the same kinematic principles apply, with the mass not affecting the kinematic calculations directly (mass affects force and energy, but not acceleration if uniform acceleration is given). If you provide the time or distance, more specific calculations can be done.
