Question

A wagon traveling initially at a speed of 20 m/s accelerates uniformly at the rate of -3 m/s² for a distance of 30 meters. The wagon's velocity after covering this distance is

a) 20 m/s
b) 5 m/s
c) 35 m/s
d) 50 m/s

Answer 1

To find the wagon's velocity after accelerating negatively over a distance of 30 meters, the kinematic equation v² = u² + 2as is used. The correct answer is approximately 14.8 m/s, which is not listed among the given options.

Step-by-step explanation:

The student's question involves a wagon slowing down due to a negative acceleration (deceleration). The initial speed is given as 20 m/s, and it accelerates at a rate of -3 m/s² over a distance of 30 meters. To find the final velocity of the wagon after covering this distance, we can use the kinematic equation:

v² = u² + 2as

Where:

v is the final velocity

u is the initial velocity (20 m/s)

a is the acceleration (-3 m/s²)

s is the distance (30 m)

Plugging in the values:

v² = (20 m/s)² + 2*(-3 m/s²)*30 m

v² = 400 m²/s² - 180 m²/s²

v² = 220 m²/s²

v = √(220 m²/s²)

v ≈ 14.8 m/s

None of the provided options (a) 20 m/s, (b) 5 m/s, (c) 35 m/s, (d) 50 m/s is correct. Therefore, the correct answer to the student's question must be approximately 14.8 m/s, which is not listed among the options.