can someone please help me with this math problem?
1 answer:
You might be interested in
Answer:
Step-by-step explanation:
Given
When mass = 4kg; Acceleration = 15m/s²
Required
Determine the acceleration when mass = 10kg, provided force is constant;
Represent mass with m and acceleration with a
The question says there's an inverse variation between acceleration and mass; This is represented as thus;
Convert variation to equality
; Where F is the constant of variation (Force)
Make F the subject of formula;
When mass = 4kg; Acceleration = 15m/s²
When mass = 10kg; Substitute 60 for Force
Divide both sides by 10
<em>Hence, the acceleration is </em><em />
Answer:
The maximum distance traveled is 4.73 meters in 0.23 seconds.
Step-by-step explanation:
We have that the distance traveled with respect to time is given by the function,
.
Now, differentiating this function with respect to time 't', we get,
d'(t)=9.8t-2.3
Equating d'(t) by 0 gives,
9.8t - 2.3 = 0
i.e. 9.8t = 2.3
i.e. t = 0.23 seconds
Substitute this value in d'(t) gives,
d'(t) = 9.8 × 0.23 - 2.3
d'(t) = 2.254 - 2.3
d'(t) = -0.046.
As, d'(t) < 0, we get that the function has the maximum value at t = 0.23 seconds.
Thus, the maximum distance the skateboard can travel is given by,
.
i.e. .
i.e. .
i.e. .
i.e. d(t) = 4.73021
Hence, the maximum distance traveled is 4.73 meters in 0.23 seconds.