Question

A car that is initially moving at 7.50 , m/s begins to accelerate forward uniformly at 0.550 , m/s^2. How far in meters has the car traveled after 100s?

a) 550 m

b) 800 m

c) 950 m

d) 1100 m

Answer 1

The distance traveled by the car after accelerating uniformly for 100s is 3500 meters. The given options in the multiple choice do not include this correct answer, suggesting a potential error in the question or options provided.

Step-by-step explanation:

The student has presented a problem involving uniform acceleration. The equation that relates initial velocity, acceleration, and distance is given by the equation s = ut + ½ at², where 's' is the distance, 'u' is the initial velocity, 't' is the time, and 'a' is the acceleration. Plugging in the values given, we do the following calculation:

'u' = 7.50 m/s (initial velocity), 'a' = 0.550 m/s² (acceleration), 't' = 100s (time)

Using the formula: s = 7.50 m/s × 100 s + ½ × 0.550 m/s² × (100 s)²

Calculating:

• s = 750 m + ½ × 0.550 m/s² × 10000 s²
• s = 750 m + 2750 m
• s = 3500 m

Thus, after 100s, the car has traveled 3500 meters.

It's important to note that the given multiple-choice options do not include the correct answer; perhaps there is a mistake in the options provided or in the interpretation of the question.