when a chameleon captures an insect its tingue car extend 16 cm in 0.10 s. (a) Find the magnitude of the tongue's acceleration, assuming it to be constant.(b) In the first 0.050 s, dones the tongue extend 8.0 cm, more than 8.0 cm, or less than 8.0 cm? Support your conclusion with a calculation.
To solve this problem, we can use the kinematic equation to calculate the acceleration of the chameleon's tongue. The equation we'll use is:
d = (vi * t) + (0.5 * a * t^2)
where:
d = displacement
vi = initial velocity
t = time
a = acceleration
(a) To find the magnitude of the tongue's acceleration, we need to rearrange the equation:
a = (2 * (d - (vi * t))) / t^2
Given:
d = 16 cm (tongue's displacement)
t = 0.10 s (time taken)
Plugging in the values:
a = (2 * (16 cm - (0 * 0.10 s))) / (0.10 s)^2
a = (32 cm) / (0.01 s^2)
a = 3200 cm/s^2
Therefore, the magnitude of the tongue's acceleration is 3200 cm/s^2.
(b) To determine whether the tongue extends more or less than 8.0 cm in the first 0.050 s, we'll use the same equation:
d = (vi * t) + (0.5 * a * t^2)
Given:
vi = 0 cm/s (initial velocity)
t = 0.050 s (time taken)
d = ? (displacement)
We need to solve for d:
d = (vi * t) + (0.5 * a * t^2)
d = (0 cm/s * 0.050 s) + (0.5 * 3200 cm/s^2 * (0.050 s)^2)
d = 0 + 4 cm
d = 4 cm
Therefore, in the first 0.050 s, the chameleon's tongue extends 4 cm, which is less than 8.0 cm.
16
2