A Thompson’s gazelle can reach a speed of 13 m/s in 3.0 s. A lion can reach a speed of 9.5 m/s in 1.0 s. A trout can reach a speed of 2.8 m/s in 0.12 s. Which animal has the greatest acceleration?
To determine which animal has the greatest acceleration, we need to compare the rate at which their speeds change over time. Acceleration is defined as the change in velocity divided by the time taken.
Acceleration (a) = (Final velocity - Initial velocity) / Time
For the Thompson's gazelle:
Final velocity (v1) = 13 m/s
Initial velocity (u1) = 0 m/s (assuming it starts from rest)
Time (t1) = 3.0 s
Using the formula, we find the acceleration of the gazelle:
a1 = (v1 - u1) / t1 = (13 m/s - 0 m/s) / 3.0 s = 4.33 m/s²
For the lion:
Final velocity (v2) = 9.5 m/s
Initial velocity (u2) = 0 m/s (assuming it starts from rest)
Time (t2) = 1.0 s
Using the formula, we find the acceleration of the lion:
a2 = (v2 - u2) / t2 = (9.5 m/s - 0 m/s) / 1.0 s = 9.5 m/s²
For the trout:
Final velocity (v3) = 2.8 m/s
Initial velocity (u3) = 0 m/s (assuming it starts from rest)
Time (t3) = 0.12 s
Using the formula, we find the acceleration of the trout:
a3 = (v3 - u3) / t3 = (2.8 m/s - 0 m/s) / 0.12 s = 23.3 m/s²
Comparing the accelerations, we can see that the trout has the greatest acceleration with 23.3 m/s².